Comparing and Identifying Fractions on a Number Line

Directions: Using the digits 1 to 9 exactly once, place a digit in each box to create and place 4 fractions on the number line in the correct order. (fractions B & C are equal)

Hint

The sum of the equivalent fractions is greater than a half and greater than a quarter separate. How do you know if two fractions are equivalent? How do you know if fractions are less than or greater than another fraction?

Answer

There are many possible answers. Here are a couple: A = 1/7, B = 3/8, C = 9/24, D = 5/6; Another possibility is A = 1/5, B = 3/9, C = 8/24, D = 6/7; yet another possibility is A = 5/8, B = 3/4, C = 9/12 and D = 6/7. (or D could be 7/6)

Source: Graham FletcherBowen Kerins, and Kate Nowak

 

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Directions: Using the digits 1 to 9 at most one time each, place a digit …

15 comments

  1. Here is another answer a student found A = 5/8, B = 3/4, C = 9/12 and D = 6/7. (or D could be 7/6)

  2. B and C are not equivalent in your first possible answer. (3/6 > 9/27)

  3. This is so much fun! My students and I are wondering about A= 3/7, B=4/8, C=6/12 and D=9/5 and A= 2/7, B=3/6, C=9/18 and D=5/4 Thanks for sharing your work with us!

  4. A group of students worked on this yesterday as they reviewed equivalent fractions and ordering…and they/we had so much fun doing! It was their first “open-middle” task with the recording sheet. I am so excited about this task. There were so many great discussions, mistakes, revisions…

  5. Another possibility…I got 3/7, 2/4, 9/18, and 5/6.

  6. My son spent a few hours seeking to find the most optimal answer based on the partitioning of the number line. He makes a case for 2/5, 3/6,7/14, 8/9. The difference or distance between 3/6 and 8/9 is approx. 4 times the distance between 2/5 and 3/6.

  7. What fun. Today we were comparing fractions to 1/2. I wanted to test this out myself before I introduced it to the class. I thought, if I make B 1/2 or its equivalent, than I can use the left over digits to create a fraction less than 1/2, and another greater than 1/2. I came up with a = 3/9, b = 2/4 = 8/16, and d = 5/7. I wonder if any of my students will think this way.

  8. I think a is 3/7, b is 2/4, d is 5/6, and c is 9/18.

  9. I really like this problem and look forward to trying it out with my students. Is the placement on the line supposed to suggest some sort of scale or do the fractions just have to be A<B=C<D?

  10. Here’s my answer

    1/8 < (3/8 & 9/24) < 1/2

  11. 1: 4, 12, 35, 69, 78
    2: 4, 12, 35, 69, 87
    3: 4, 12, 35, 76, 98
    4: 4, 12, 35, 78, 96
    5: 4, 12, 35, 87, 96
    6: 4, 12, 36, 57, 98
    7: 4, 12, 36, 75, 98
    8: 4, 12, 36, 78, 95
    9: 4, 12, 36, 87, 95
    10: 4, 12, 38, 57, 69
    11: 4, 12, 38, 57, 96
    12: 4, 12, 38, 69, 75
    13: 4, 12, 38, 75, 96
    14: 4, 12, 38, 76, 95
    15: 4, 12, 39, 56, 78
    16: 4, 12, 39, 56, 87
    17: 4, 12, 39, 57, 68
    18: 4, 12, 39, 57, 86
    19: 4, 12, 39, 58, 76
    20: 4, 12, 39, 65, 78
    21: 4, 12, 39, 65, 87
    22: 4, 12, 39, 68, 75
    23: 4, 12, 39, 75, 86
    24: 4, 12, 39, 76, 85
    25: 4, 12, 56, 78, 93
    26: 4, 12, 56, 87, 93
    27: 4, 12, 57, 63, 98
    28: 4, 12, 57, 68, 93
    29: 4, 12, 57, 86, 93
    30: 4, 12, 58, 76, 93
    31: 4, 12, 63, 75, 98
    32: 4, 12, 63, 78, 95
    33: 4, 12, 63, 87, 95
    34: 4, 12, 65, 78, 93
    35: 4, 12, 65, 87, 93
    36: 4, 12, 68, 75, 93
    37: 4, 12, 75, 86, 93
    38: 4, 12, 76, 85, 93
    39: 4, 15, 26, 39, 78
    40: 4, 15, 26, 39, 87
    41: 4, 15, 26, 78, 93
    42: 4, 15, 26, 87, 93
    43: 4, 15, 27, 36, 98
    44: 4, 15, 27, 38, 69
    45: 4, 15, 27, 38, 96
    46: 4, 15, 27, 39, 68
    47: 4, 15, 27, 39, 86
    48: 4, 15, 27, 63, 98
    49: 4, 15, 27, 68, 93
    50: 4, 15, 27, 86, 93
    51: 4, 15, 28, 39, 76
    52: 4, 15, 28, 76, 93
    53: 4, 15, 32, 69, 78
    54: 4, 15, 32, 69, 87
    55: 4, 15, 32, 76, 98
    56: 4, 15, 32, 78, 96
    57: 4, 15, 32, 87, 96
    58: 4, 15, 36, 72, 98
    59: 4, 15, 36, 78, 92
    60: 4, 15, 36, 87, 92
    61: 4, 15, 38, 69, 72
    62: 4, 15, 38, 72, 96
    63: 4, 15, 38, 76, 92
    64: 4, 15, 39, 62, 78
    65: 4, 15, 39, 62, 87
    66: 4, 15, 39, 68, 72
    67: 4, 15, 39, 72, 86
    68: 4, 15, 39, 76, 82
    69: 4, 15, 62, 78, 93
    70: 4, 15, 62, 87, 93
    71: 4, 15, 63, 72, 98
    72: 4, 15, 63, 78, 92
    73: 4, 15, 63, 87, 92
    74: 4, 15, 68, 72, 93
    75: 4, 15, 72, 86, 93
    76: 4, 15, 76, 82, 93
    77: 4, 16, 25, 39, 78
    78: 4, 16, 25, 39, 87
    79: 4, 16, 25, 78, 93
    80: 4, 16, 25, 87, 93
    81: 4, 16, 27, 35, 98
    82: 4, 16, 27, 38, 95
    83: 4, 16, 27, 39, 58
    84: 4, 16, 27, 39, 85
    85: 4, 16, 27, 58, 93
    86: 4, 16, 27, 85, 93
    87: 4, 16, 28, 39, 57
    88: 4, 16, 28, 39, 75
    89: 4, 16, 28, 57, 93
    90: 4, 16, 28, 75, 93
    91: 4, 16, 32, 57, 98
    92: 4, 16, 32, 75, 98
    93: 4, 16, 32, 78, 95
    94: 4, 16, 32, 87, 95
    95: 4, 16, 35, 72, 98
    96: 4, 16, 35, 78, 92
    97: 4, 16, 35, 87, 92
    98: 4, 16, 38, 57, 92
    99: 4, 16, 38, 72, 95
    100: 4, 16, 38, 75, 92
    101: 4, 16, 39, 52, 78
    102: 4, 16, 39, 52, 87
    103: 4, 16, 39, 57, 82
    104: 4, 16, 39, 58, 72
    105: 4, 16, 39, 72, 85
    106: 4, 16, 39, 75, 82
    107: 4, 16, 52, 78, 93
    108: 4, 16, 52, 87, 93
    109: 4, 16, 57, 82, 93
    110: 4, 16, 58, 72, 93
    111: 4, 16, 72, 85, 93
    112: 4, 16, 75, 82, 93
    113: 4, 18, 25, 39, 76
    114: 4, 18, 25, 76, 93
    115: 4, 18, 26, 39, 57
    116: 4, 18, 26, 39, 75
    117: 4, 18, 26, 57, 93
    118: 4, 18, 26, 75, 93
    119: 4, 18, 27, 35, 69
    120: 4, 18, 27, 35, 96
    121: 4, 18, 27, 36, 95
    122: 4, 18, 27, 39, 56
    123: 4, 18, 27, 39, 65
    124: 4, 18, 27, 56, 93
    125: 4, 18, 27, 63, 95
    126: 4, 18, 27, 65, 93
    127: 4, 18, 32, 57, 69
    128: 4, 18, 32, 57, 96
    129: 4, 18, 32, 69, 75
    130: 4, 18, 32, 75, 96
    131: 4, 18, 32, 76, 95
    132: 4, 18, 35, 69, 72
    133: 4, 18, 35, 72, 96
    134: 4, 18, 35, 76, 92
    135: 4, 18, 36, 57, 92
    136: 4, 18, 36, 72, 95
    137: 4, 18, 36, 75, 92
    138: 4, 18, 39, 52, 76
    139: 4, 18, 39, 56, 72
    140: 4, 18, 39, 57, 62
    141: 4, 18, 39, 62, 75
    142: 4, 18, 39, 65, 72
    143: 4, 18, 52, 76, 93
    144: 4, 18, 56, 72, 93
    145: 4, 18, 57, 62, 93
    146: 4, 18, 57, 63, 92
    147: 4, 18, 62, 75, 93
    148: 4, 18, 63, 72, 95
    149: 4, 18, 63, 75, 92
    150: 4, 18, 65, 72, 93
    151: 4, 21, 35, 69, 78
    152: 4, 21, 35, 69, 87
    153: 4, 21, 35, 76, 98
    154: 4, 21, 35, 78, 96
    155: 4, 21, 35, 87, 96
    156: 4, 21, 36, 57, 98
    157: 4, 21, 36, 75, 98
    158: 4, 21, 36, 78, 95
    159: 4, 21, 36, 87, 95
    160: 4, 21, 38, 57, 69
    161: 4, 21, 38, 57, 96
    162: 4, 21, 38, 69, 75
    163: 4, 21, 38, 75, 96
    164: 4, 21, 38, 76, 95
    165: 4, 21, 39, 56, 78
    166: 4, 21, 39, 56, 87
    167: 4, 21, 39, 57, 68
    168: 4, 21, 39, 57, 86
    169: 4, 21, 39, 58, 76
    170: 4, 21, 39, 65, 78
    171: 4, 21, 39, 65, 87
    172: 4, 21, 39, 68, 75
    173: 4, 21, 39, 75, 86
    174: 4, 21, 39, 76, 85
    175: 4, 21, 56, 78, 93
    176: 4, 21, 56, 87, 93
    177: 4, 21, 57, 63, 98
    178: 4, 21, 57, 68, 93
    179: 4, 21, 57, 86, 93
    180: 4, 21, 58, 76, 93
    181: 4, 21, 63, 75, 98
    182: 4, 21, 63, 78, 95
    183: 4, 21, 63, 87, 95
    184: 4, 21, 65, 78, 93
    185: 4, 21, 65, 87, 93
    186: 4, 21, 68, 75, 93
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    188: 4, 21, 76, 85, 93
    189: 4, 25, 36, 78, 91
    190: 4, 25, 36, 87, 91
    191: 4, 25, 38, 76, 91
    192: 4, 25, 39, 76, 81
    193: 4, 25, 63, 78, 91
    194: 4, 25, 63, 87, 91
    195: 4, 25, 76, 81, 93
    196: 4, 26, 35, 78, 91
    197: 4, 26, 35, 87, 91
    198: 4, 26, 38, 57, 91
    199: 4, 26, 38, 75, 91
    200: 4, 26, 39, 51, 78
    201: 4, 26, 39, 51, 87
    202: 4, 26, 39, 57, 81
    203: 4, 26, 39, 75, 81
    204: 4, 26, 51, 78, 93
    205: 4, 26, 51, 87, 93
    206: 4, 26, 57, 81, 93
    207: 4, 26, 75, 81, 93
    208: 4, 27, 35, 68, 91
    209: 4, 27, 35, 69, 81
    210: 4, 27, 35, 81, 96
    211: 4, 27, 35, 86, 91
    212: 4, 27, 36, 51, 98
    213: 4, 27, 36, 58, 91
    214: 4, 27, 36, 81, 95
    215: 4, 27, 36, 85, 91
    216: 4, 27, 38, 51, 69
    217: 4, 27, 38, 51, 96
    218: 4, 27, 38, 56, 91
    219: 4, 27, 38, 65, 91
    220: 4, 27, 39, 51, 68
    221: 4, 27, 39, 51, 86
    222: 4, 27, 39, 56, 81
    223: 4, 27, 39, 65, 81
    224: 4, 27, 51, 63, 98
    225: 4, 27, 51, 68, 93
    226: 4, 27, 51, 86, 93
    227: 4, 27, 56, 81, 93
    228: 4, 27, 58, 63, 91
    229: 4, 27, 63, 81, 95
    230: 4, 27, 63, 85, 91
    231: 4, 27, 65, 81, 93
    232: 4, 28, 35, 76, 91
    233: 4, 28, 36, 57, 91
    234: 4, 28, 36, 75, 91
    235: 4, 28, 39, 51, 76
    236: 4, 28, 51, 76, 93
    237: 4, 28, 57, 63, 91
    238: 4, 28, 63, 75, 91
    239: 4, 32, 51, 69, 78
    240: 4, 32, 51, 69, 87
    241: 4, 32, 51, 76, 98
    242: 4, 32, 51, 78, 96
    243: 4, 32, 51, 87, 96
    244: 4, 32, 56, 78, 91
    245: 4, 32, 56, 87, 91
    246: 4, 32, 57, 68, 91
    247: 4, 32, 57, 69, 81
    248: 4, 32, 57, 81, 96
    249: 4, 32, 57, 86, 91
    250: 4, 32, 58, 76, 91
    251: 4, 32, 65, 78, 91
    252: 4, 32, 65, 87, 91
    253: 4, 32, 68, 75, 91
    254: 4, 32, 69, 75, 81
    255: 4, 32, 75, 81, 96
    256: 4, 32, 75, 86, 91
    257: 4, 32, 76, 81, 95
    258: 4, 32, 76, 85, 91
    259: 4, 35, 62, 78, 91
    260: 4, 35, 62, 87, 91
    261: 4, 35, 68, 72, 91
    262: 4, 35, 69, 72, 81
    263: 4, 35, 72, 81, 96
    264: 4, 35, 72, 86, 91
    265: 4, 35, 76, 81, 92
    266: 4, 35, 76, 82, 91
    267: 4, 36, 51, 72, 98
    268: 4, 36, 51, 78, 92
    269: 4, 36, 51, 87, 92
    270: 4, 36, 52, 78, 91
    271: 4, 36, 52, 87, 91
    272: 4, 36, 57, 81, 92
    273: 4, 36, 57, 82, 91
    274: 4, 36, 58, 72, 91
    275: 4, 36, 72, 81, 95
    276: 4, 36, 72, 85, 91
    277: 4, 36, 75, 81, 92
    278: 4, 36, 75, 82, 91
    279: 4, 38, 51, 69, 72
    280: 4, 38, 51, 72, 96
    281: 4, 38, 51, 76, 92
    282: 4, 38, 52, 76, 91
    283: 4, 38, 56, 72, 91
    284: 4, 38, 57, 62, 91
    285: 4, 38, 62, 75, 91
    286: 4, 38, 65, 72, 91
    287: 4, 39, 51, 62, 78
    288: 4, 39, 51, 62, 87
    289: 4, 39, 51, 68, 72
    290: 4, 39, 51, 72, 86
    291: 4, 39, 51, 76, 82
    292: 4, 39, 52, 76, 81
    293: 4, 39, 56, 72, 81
    294: 4, 39, 57, 62, 81
    295: 4, 39, 62, 75, 81
    296: 4, 39, 65, 72, 81
    297: 4, 51, 62, 78, 93
    298: 4, 51, 62, 87, 93
    299: 4, 51, 63, 72, 98
    300: 4, 51, 63, 78, 92
    301: 4, 51, 63, 87, 92
    302: 4, 51, 68, 72, 93
    303: 4, 51, 72, 86, 93
    304: 4, 51, 76, 82, 93
    305: 4, 52, 63, 78, 91
    306: 4, 52, 63, 87, 91
    307: 4, 52, 76, 81, 93
    308: 4, 56, 72, 81, 93
    309: 4, 57, 62, 81, 93
    310: 4, 57, 63, 81, 92
    311: 4, 57, 63, 82, 91
    312: 4, 58, 63, 72, 91
    313: 4, 62, 75, 81, 93
    314: 4, 63, 72, 81, 95
    315: 4, 63, 72, 85, 91
    316: 4, 63, 75, 81, 92
    317: 4, 63, 75, 82, 91
    318: 4, 65, 72, 81, 93
    319: 6, 12, 34, 57, 98
    320: 6, 12, 34, 75, 98
    321: 6, 12, 34, 78, 95
    322: 6, 12, 34, 87, 95
    323: 6, 12, 35, 49, 78
    324: 6, 12, 35, 49, 87
    325: 6, 12, 35, 74, 98
    326: 6, 12, 35, 78, 94
    327: 6, 12, 35, 87, 94
    328: 6, 12, 38, 49, 57
    329: 6, 12, 38, 49, 75
    330: 6, 12, 38, 57, 94
    331: 6, 12, 38, 74, 95
    332: 6, 12, 38, 75, 94
    333: 6, 12, 39, 45, 78
    334: 6, 12, 39, 45, 87
    335: 6, 12, 39, 48, 57
    336: 6, 12, 39, 48, 75
    337: 6, 12, 39, 54, 78
    338: 6, 12, 39, 54, 87
    339: 6, 12, 39, 57, 84
    340: 6, 12, 39, 58, 74
    341: 6, 12, 39, 74, 85
    342: 6, 12, 39, 75, 84
    343: 6, 12, 45, 78, 93
    344: 6, 12, 45, 87, 93
    345: 6, 12, 48, 57, 93
    346: 6, 12, 48, 75, 93
    347: 6, 12, 54, 78, 93
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    349: 6, 12, 57, 84, 93
    350: 6, 12, 58, 74, 93
    351: 6, 12, 74, 85, 93
    352: 6, 12, 75, 84, 93
    353: 6, 14, 25, 39, 78
    354: 6, 14, 25, 39, 87
    355: 6, 14, 25, 78, 93
    356: 6, 14, 25, 87, 93
    357: 6, 14, 27, 35, 98
    358: 6, 14, 27, 38, 95
    359: 6, 14, 27, 39, 58
    360: 6, 14, 27, 39, 85
    361: 6, 14, 27, 58, 93
    362: 6, 14, 27, 85, 93
    363: 6, 14, 28, 39, 57
    364: 6, 14, 28, 39, 75
    365: 6, 14, 28, 57, 93
    366: 6, 14, 28, 75, 93
    367: 6, 14, 32, 57, 98
    368: 6, 14, 32, 75, 98
    369: 6, 14, 32, 78, 95
    370: 6, 14, 32, 87, 95
    371: 6, 14, 35, 72, 98
    372: 6, 14, 35, 78, 92
    373: 6, 14, 35, 87, 92
    374: 6, 14, 38, 57, 92
    375: 6, 14, 38, 72, 95
    376: 6, 14, 38, 75, 92
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    378: 6, 14, 39, 52, 87
    379: 6, 14, 39, 57, 82
    380: 6, 14, 39, 58, 72
    381: 6, 14, 39, 72, 85
    382: 6, 14, 39, 75, 82
    383: 6, 14, 52, 78, 93
    384: 6, 14, 52, 87, 93
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    386: 6, 14, 58, 72, 93
    387: 6, 14, 72, 85, 93
    388: 6, 14, 75, 82, 93
    389: 6, 15, 24, 39, 78
    390: 6, 15, 24, 39, 87
    391: 6, 15, 24, 78, 93
    392: 6, 15, 24, 87, 93
    393: 6, 15, 27, 34, 98
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    395: 6, 15, 27, 38, 94
    396: 6, 15, 27, 39, 48
    397: 6, 15, 27, 39, 84
    398: 6, 15, 27, 48, 93
    399: 6, 15, 27, 84, 93
    400: 6, 15, 28, 39, 74
    401: 6, 15, 28, 74, 93
    402: 6, 15, 32, 49, 78
    403: 6, 15, 32, 49, 87
    404: 6, 15, 32, 74, 98
    405: 6, 15, 32, 78, 94
    406: 6, 15, 32, 87, 94
    407: 6, 15, 34, 72, 98
    408: 6, 15, 34, 78, 92
    409: 6, 15, 34, 87, 92
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    411: 6, 15, 38, 72, 94
    412: 6, 15, 38, 74, 92
    413: 6, 15, 39, 42, 78
    414: 6, 15, 39, 42, 87
    415: 6, 15, 39, 48, 72
    416: 6, 15, 39, 72, 84
    417: 6, 15, 39, 74, 82
    418: 6, 15, 42, 78, 93
    419: 6, 15, 42, 87, 93
    420: 6, 15, 48, 72, 93
    421: 6, 15, 72, 84, 93
    422: 6, 15, 74, 82, 93
    423: 6, 18, 24, 39, 57
    424: 6, 18, 24, 39, 75
    425: 6, 18, 24, 57, 93
    426: 6, 18, 24, 75, 93
    427: 6, 18, 25, 39, 74
    428: 6, 18, 25, 74, 93
    429: 6, 18, 27, 34, 95
    430: 6, 18, 27, 35, 49
    431: 6, 18, 27, 35, 94
    432: 6, 18, 27, 39, 45
    433: 6, 18, 27, 39, 54
    434: 6, 18, 27, 45, 93
    435: 6, 18, 27, 54, 93
    436: 6, 18, 32, 49, 57
    437: 6, 18, 32, 49, 75
    438: 6, 18, 32, 57, 94
    439: 6, 18, 32, 74, 95
    440: 6, 18, 32, 75, 94
    441: 6, 18, 34, 57, 92
    442: 6, 18, 34, 72, 95
    443: 6, 18, 34, 75, 92
    444: 6, 18, 35, 49, 72
    445: 6, 18, 35, 72, 94
    446: 6, 18, 35, 74, 92
    447: 6, 18, 39, 42, 57
    448: 6, 18, 39, 42, 75
    449: 6, 18, 39, 45, 72
    450: 6, 18, 39, 52, 74
    451: 6, 18, 39, 54, 72
    452: 6, 18, 42, 57, 93
    453: 6, 18, 42, 75, 93
    454: 6, 18, 45, 72, 93
    455: 6, 18, 52, 74, 93
    456: 6, 18, 54, 72, 93
    457: 6, 21, 34, 57, 98
    458: 6, 21, 34, 75, 98
    459: 6, 21, 34, 78, 95
    460: 6, 21, 34, 87, 95
    461: 6, 21, 35, 49, 78
    462: 6, 21, 35, 49, 87
    463: 6, 21, 35, 74, 98
    464: 6, 21, 35, 78, 94
    465: 6, 21, 35, 87, 94
    466: 6, 21, 38, 49, 57
    467: 6, 21, 38, 49, 75
    468: 6, 21, 38, 57, 94
    469: 6, 21, 38, 74, 95
    470: 6, 21, 38, 75, 94
    471: 6, 21, 39, 45, 78
    472: 6, 21, 39, 45, 87
    473: 6, 21, 39, 48, 57
    474: 6, 21, 39, 48, 75
    475: 6, 21, 39, 54, 78
    476: 6, 21, 39, 54, 87
    477: 6, 21, 39, 57, 84
    478: 6, 21, 39, 58, 74
    479: 6, 21, 39, 74, 85
    480: 6, 21, 39, 75, 84
    481: 6, 21, 45, 78, 93
    482: 6, 21, 45, 87, 93
    483: 6, 21, 48, 57, 93
    484: 6, 21, 48, 75, 93
    485: 6, 21, 54, 78, 93
    486: 6, 21, 54, 87, 93
    487: 6, 21, 57, 84, 93
    488: 6, 21, 58, 74, 93
    489: 6, 21, 74, 85, 93
    490: 6, 21, 75, 84, 93
    491: 6, 24, 35, 78, 91
    492: 6, 24, 35, 87, 91
    493: 6, 24, 38, 57, 91
    494: 6, 24, 38, 75, 91
    495: 6, 24, 39, 51, 78
    496: 6, 24, 39, 51, 87
    497: 6, 24, 39, 57, 81
    498: 6, 24, 39, 75, 81
    499: 6, 24, 51, 78, 93
    500: 6, 24, 51, 87, 93
    501: 6, 24, 57, 81, 93
    502: 6, 24, 75, 81, 93
    503: 6, 25, 34, 78, 91
    504: 6, 25, 34, 87, 91
    505: 6, 25, 38, 74, 91
    506: 6, 25, 39, 74, 81
    507: 6, 25, 74, 81, 93
    508: 6, 27, 34, 51, 98
    509: 6, 27, 34, 58, 91
    510: 6, 27, 34, 81, 95
    511: 6, 27, 34, 85, 91
    512: 6, 27, 35, 48, 91
    513: 6, 27, 35, 49, 81
    514: 6, 27, 35, 81, 94
    515: 6, 27, 35, 84, 91
    516: 6, 27, 38, 45, 91
    517: 6, 27, 38, 49, 51
    518: 6, 27, 38, 51, 94
    519: 6, 27, 38, 54, 91
    520: 6, 27, 39, 45, 81
    521: 6, 27, 39, 48, 51
    522: 6, 27, 39, 51, 84
    523: 6, 27, 39, 54, 81
    524: 6, 27, 45, 81, 93
    525: 6, 27, 48, 51, 93
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    1096: 9, 21, 34, 57, 86
    1097: 9, 21, 34, 58, 76
    1098: 9, 21, 34, 65, 78
    1099: 9, 21, 34, 65, 87
    1100: 9, 21, 34, 68, 75
    1101: 9, 21, 34, 75, 86
    1102: 9, 21, 34, 76, 85
    1103: 9, 21, 35, 46, 78
    1104: 9, 21, 35, 46, 87
    1105: 9, 21, 35, 48, 76
    1106: 9, 21, 35, 64, 78
    1107: 9, 21, 35, 64, 87
    1108: 9, 21, 35, 68, 74
    1109: 9, 21, 35, 74, 86
    1110: 9, 21, 35, 76, 84
    1111: 9, 21, 36, 45, 78
    1112: 9, 21, 36, 45, 87
    1113: 9, 21, 36, 48, 57
    1114: 9, 21, 36, 48, 75
    1115: 9, 21, 36, 54, 78
    1116: 9, 21, 36, 54, 87
    1117: 9, 21, 36, 57, 84
    1118: 9, 21, 36, 58, 74
    1119: 9, 21, 36, 74, 85
    1120: 9, 21, 36, 75, 84
    1121: 9, 21, 38, 45, 76
    1122: 9, 21, 38, 46, 57
    1123: 9, 21, 38, 46, 75
    1124: 9, 21, 38, 54, 76
    1125: 9, 21, 38, 56, 74
    1126: 9, 21, 38, 57, 64
    1127: 9, 21, 38, 64, 75
    1128: 9, 21, 38, 65, 74
    1129: 9, 21, 45, 63, 78
    1130: 9, 21, 45, 63, 87
    1131: 9, 21, 48, 57, 63
    1132: 9, 21, 48, 63, 75
    1133: 9, 21, 54, 63, 78
    1134: 9, 21, 54, 63, 87
    1135: 9, 21, 57, 63, 84
    1136: 9, 21, 58, 63, 74
    1137: 9, 21, 63, 74, 85
    1138: 9, 21, 63, 75, 84
    1139: 9, 24, 35, 76, 81
    1140: 9, 24, 36, 51, 78
    1141: 9, 24, 36, 51, 87
    1142: 9, 24, 36, 57, 81
    1143: 9, 24, 36, 75, 81
    1144: 9, 24, 38, 51, 76
    1145: 9, 24, 51, 63, 78
    1146: 9, 24, 51, 63, 87
    1147: 9, 24, 57, 63, 81
    1148: 9, 24, 63, 75, 81
    1149: 9, 25, 34, 76, 81
    1150: 9, 25, 36, 74, 81
    1151: 9, 25, 63, 74, 81
    1152: 9, 26, 34, 51, 78
    1153: 9, 26, 34, 51, 87
    1154: 9, 26, 34, 57, 81
    1155: 9, 26, 34, 75, 81
    1156: 9, 26, 35, 74, 81
    1157: 9, 26, 38, 51, 74
    1158: 9, 27, 34, 51, 68
    1159: 9, 27, 34, 51, 86
    1160: 9, 27, 34, 56, 81
    1161: 9, 27, 34, 65, 81
    1162: 9, 27, 35, 46, 81
    1163: 9, 27, 35, 64, 81
    1164: 9, 27, 36, 45, 81
    1165: 9, 27, 36, 48, 51
    1166: 9, 27, 36, 51, 84
    1167: 9, 27, 36, 54, 81
    1168: 9, 27, 38, 46, 51
    1169: 9, 27, 38, 51, 64
    1170: 9, 27, 45, 63, 81
    1171: 9, 27, 48, 51, 63
    1172: 9, 27, 51, 63, 84
    1173: 9, 27, 54, 63, 81
    1174: 9, 28, 34, 51, 76
    1175: 9, 28, 36, 51, 74
    1176: 9, 28, 51, 63, 74
    1177: 9, 32, 45, 76, 81
    1178: 9, 32, 46, 51, 78
    1179: 9, 32, 46, 51, 87
    1180: 9, 32, 46, 57, 81
    1181: 9, 32, 46, 75, 81
    1182: 9, 32, 48, 51, 76
    1183: 9, 32, 51, 64, 78
    1184: 9, 32, 51, 64, 87
    1185: 9, 32, 51, 68, 74
    1186: 9, 32, 51, 74, 86
    1187: 9, 32, 51, 76, 84
    1188: 9, 32, 54, 76, 81
    1189: 9, 32, 56, 74, 81
    1190: 9, 32, 57, 64, 81
    1191: 9, 32, 64, 75, 81
    1192: 9, 32, 65, 74, 81
    1193: 9, 34, 51, 62, 78
    1194: 9, 34, 51, 62, 87
    1195: 9, 34, 51, 68, 72
    1196: 9, 34, 51, 72, 86
    1197: 9, 34, 51, 76, 82
    1198: 9, 34, 52, 76, 81
    1199: 9, 34, 56, 72, 81
    1200: 9, 34, 57, 62, 81
    1201: 9, 34, 62, 75, 81
    1202: 9, 34, 65, 72, 81
    1203: 9, 35, 42, 76, 81
    1204: 9, 35, 46, 72, 81
    1205: 9, 35, 62, 74, 81
    1206: 9, 35, 64, 72, 81
    1207: 9, 36, 42, 51, 78
    1208: 9, 36, 42, 51, 87
    1209: 9, 36, 42, 57, 81
    1210: 9, 36, 42, 75, 81
    1211: 9, 36, 45, 72, 81
    1212: 9, 36, 48, 51, 72
    1213: 9, 36, 51, 72, 84
    1214: 9, 36, 51, 74, 82
    1215: 9, 36, 52, 74, 81
    1216: 9, 36, 54, 72, 81
    1217: 9, 38, 42, 51, 76
    1218: 9, 38, 46, 51, 72
    1219: 9, 38, 51, 62, 74
    1220: 9, 38, 51, 64, 72
    1221: 9, 42, 51, 63, 78
    1222: 9, 42, 51, 63, 87
    1223: 9, 42, 57, 63, 81
    1224: 9, 42, 63, 75, 81
    1225: 9, 45, 63, 72, 81
    1226: 9, 48, 51, 63, 72
    1227: 9, 51, 63, 72, 84
    1228: 9, 51, 63, 74, 82
    1229: 9, 52, 63, 74, 81
    1230: 9, 54, 63, 72, 81
    1: 4, 12, 35, 69, 78
    2: 4, 12, 35, 69, 87
    3: 4, 12, 35, 76, 98
    4: 4, 12, 35, 78, 96
    5: 4, 12, 35, 87, 96
    6: 4, 12, 36, 57, 98
    7: 4, 12, 36, 75, 98
    8: 4, 12, 36, 78, 95
    9: 4, 12, 36, 87, 95
    10: 4, 12, 38, 57, 69
    11: 4, 12, 38, 57, 96
    12: 4, 12, 38, 69, 75
    13: 4, 12, 38, 75, 96
    14: 4, 12, 38, 76, 95
    15: 4, 12, 39, 56, 78
    16: 4, 12, 39, 56, 87
    17: 4, 12, 39, 57, 68
    18: 4, 12, 39, 57, 86
    19: 4, 12, 39, 58, 76
    20: 4, 12, 39, 65, 78
    21: 4, 12, 39, 65, 87
    22: 4, 12, 39, 68, 75
    23: 4, 12, 39, 75, 86
    24: 4, 12, 39, 76, 85
    25: 4, 12, 56, 78, 93
    26: 4, 12, 56, 87, 93
    27: 4, 12, 57, 63, 98
    28: 4, 12, 57, 68, 93
    29: 4, 12, 57, 86, 93
    30: 4, 12, 58, 76, 93
    31: 4, 12, 63, 75, 98
    32: 4, 12, 63, 78, 95
    33: 4, 12, 63, 87, 95
    34: 4, 12, 65, 78, 93
    35: 4, 12, 65, 87, 93
    36: 4, 12, 68, 75, 93
    37: 4, 12, 75, 86, 93
    38: 4, 12, 76, 85, 93
    39: 4, 15, 26, 39, 78
    40: 4, 15, 26, 39, 87
    41: 4, 15, 26, 78, 93
    42: 4, 15, 26, 87, 93
    43: 4, 15, 27, 36, 98
    44: 4, 15, 27, 38, 69
    45: 4, 15, 27, 38, 96
    46: 4, 15, 27, 39, 68
    47: 4, 15, 27, 39, 86
    48: 4, 15, 27, 63, 98
    49: 4, 15, 27, 68, 93
    50: 4, 15, 27, 86, 93
    51: 4, 15, 28, 39, 76
    52: 4, 15, 28, 76, 93
    53: 4, 15, 32, 69, 78
    54: 4, 15, 32, 69, 87
    55: 4, 15, 32, 76, 98
    56: 4, 15, 32, 78, 96
    57: 4, 15, 32, 87, 96
    58: 4, 15, 36, 72, 98
    59: 4, 15, 36, 78, 92
    60: 4, 15, 36, 87, 92
    61: 4, 15, 38, 69, 72
    62: 4, 15, 38, 72, 96
    63: 4, 15, 38, 76, 92
    64: 4, 15, 39, 62, 78
    65: 4, 15, 39, 62, 87
    66: 4, 15, 39, 68, 72
    67: 4, 15, 39, 72, 86
    68: 4, 15, 39, 76, 82
    69: 4, 15, 62, 78, 93
    70: 4, 15, 62, 87, 93
    71: 4, 15, 63, 72, 98
    72: 4, 15, 63, 78, 92
    73: 4, 15, 63, 87, 92
    74: 4, 15, 68, 72, 93
    75: 4, 15, 72, 86, 93
    76: 4, 15, 76, 82, 93
    77: 4, 16, 25, 39, 78
    78: 4, 16, 25, 39, 87
    79: 4, 16, 25, 78, 93
    80: 4, 16, 25, 87, 93
    81: 4, 16, 27, 35, 98
    82: 4, 16, 27, 38, 95
    83: 4, 16, 27, 39, 58
    84: 4, 16, 27, 39, 85
    85: 4, 16, 27, 58, 93
    86: 4, 16, 27, 85, 93
    87: 4, 16, 28, 39, 57
    88: 4, 16, 28, 39, 75
    89: 4, 16, 28, 57, 93
    90: 4, 16, 28, 75, 93
    91: 4, 16, 32, 57, 98
    92: 4, 16, 32, 75, 98
    93: 4, 16, 32, 78, 95
    94: 4, 16, 32, 87, 95
    95: 4, 16, 35, 72, 98
    96: 4, 16, 35, 78, 92
    97: 4, 16, 35, 87, 92
    98: 4, 16, 38, 57, 92
    99: 4, 16, 38, 72, 95
    100: 4, 16, 38, 75, 92
    101: 4, 16, 39, 52, 78
    102: 4, 16, 39, 52, 87
    103: 4, 16, 39, 57, 82
    104: 4, 16, 39, 58, 72
    105: 4, 16, 39, 72, 85
    106: 4, 16, 39, 75, 82
    107: 4, 16, 52, 78, 93
    108: 4, 16, 52, 87, 93
    109: 4, 16, 57, 82, 93
    110: 4, 16, 58, 72, 93
    111: 4, 16, 72, 85, 93
    112: 4, 16, 75, 82, 93
    113: 4, 18, 25, 39, 76
    114: 4, 18, 25, 76, 93
    115: 4, 18, 26, 39, 57
    116: 4, 18, 26, 39, 75
    117: 4, 18, 26, 57, 93
    118: 4, 18, 26, 75, 93
    119: 4, 18, 27, 35, 69
    120: 4, 18, 27, 35, 96
    121: 4, 18, 27, 36, 95
    122: 4, 18, 27, 39, 56
    123: 4, 18, 27, 39, 65
    124: 4, 18, 27, 56, 93
    125: 4, 18, 27, 63, 95
    126: 4, 18, 27, 65, 93
    127: 4, 18, 32, 57, 69
    128: 4, 18, 32, 57, 96
    129: 4, 18, 32, 69, 75
    130: 4, 18, 32, 75, 96
    131: 4, 18, 32, 76, 95
    132: 4, 18, 35, 69, 72
    133: 4, 18, 35, 72, 96
    134: 4, 18, 35, 76, 92
    135: 4, 18, 36, 57, 92
    136: 4, 18, 36, 72, 95
    137: 4, 18, 36, 75, 92
    138: 4, 18, 39, 52, 76
    139: 4, 18, 39, 56, 72
    140: 4, 18, 39, 57, 62
    141: 4, 18, 39, 62, 75
    142: 4, 18, 39, 65, 72
    143: 4, 18, 52, 76, 93
    144: 4, 18, 56, 72, 93
    145: 4, 18, 57, 62, 93
    146: 4, 18, 57, 63, 92
    147: 4, 18, 62, 75, 93
    148: 4, 18, 63, 72, 95
    149: 4, 18, 63, 75, 92
    150: 4, 18, 65, 72, 93
    151: 4, 21, 35, 69, 78
    152: 4, 21, 35, 69, 87
    153: 4, 21, 35, 76, 98
    154: 4, 21, 35, 78, 96
    155: 4, 21, 35, 87, 96
    156: 4, 21, 36, 57, 98
    157: 4, 21, 36, 75, 98
    158: 4, 21, 36, 78, 95
    159: 4, 21, 36, 87, 95
    160: 4, 21, 38, 57, 69
    161: 4, 21, 38, 57, 96
    162: 4, 21, 38, 69, 75
    163: 4, 21, 38, 75, 96
    164: 4, 21, 38, 76, 95
    165: 4, 21, 39, 56, 78
    166: 4, 21, 39, 56, 87
    167: 4, 21, 39, 57, 68
    168: 4, 21, 39, 57, 86
    169: 4, 21, 39, 58, 76
    170: 4, 21, 39, 65, 78
    171: 4, 21, 39, 65, 87
    172: 4, 21, 39, 68, 75
    173: 4, 21, 39, 75, 86
    174: 4, 21, 39, 76, 85
    175: 4, 21, 56, 78, 93
    176: 4, 21, 56, 87, 93
    177: 4, 21, 57, 63, 98
    178: 4, 21, 57, 68, 93
    179: 4, 21, 57, 86, 93
    180: 4, 21, 58, 76, 93
    181: 4, 21, 63, 75, 98
    182: 4, 21, 63, 78, 95
    183: 4, 21, 63, 87, 95
    184: 4, 21, 65, 78, 93
    185: 4, 21, 65, 87, 93
    186: 4, 21, 68, 75, 93
    187: 4, 21, 75, 86, 93
    188: 4, 21, 76, 85, 93
    189: 4, 25, 36, 78, 91
    190: 4, 25, 36, 87, 91
    191: 4, 25, 38, 76, 91
    192: 4, 25, 39, 76, 81
    193: 4, 25, 63, 78, 91
    194: 4, 25, 63, 87, 91
    195: 4, 25, 76, 81, 93
    196: 4, 26, 35, 78, 91
    197: 4, 26, 35, 87, 91
    198: 4, 26, 38, 57, 91
    199: 4, 26, 38, 75, 91
    200: 4, 26, 39, 51, 78
    201: 4, 26, 39, 51, 87
    202: 4, 26, 39, 57, 81
    203: 4, 26, 39, 75, 81
    204: 4, 26, 51, 78, 93
    205: 4, 26, 51, 87, 93
    206: 4, 26, 57, 81, 93
    207: 4, 26, 75, 81, 93
    208: 4, 27, 35, 68, 91
    209: 4, 27, 35, 69, 81
    210: 4, 27, 35, 81, 96
    211: 4, 27, 35, 86, 91
    212: 4, 27, 36, 51, 98
    213: 4, 27, 36, 58, 91
    214: 4, 27, 36, 81, 95
    215: 4, 27, 36, 85, 91
    216: 4, 27, 38, 51, 69
    217: 4, 27, 38, 51, 96
    218: 4, 27, 38, 56, 91
    219: 4, 27, 38, 65, 91
    220: 4, 27, 39, 51, 68
    221: 4, 27, 39, 51, 86
    222: 4, 27, 39, 56, 81
    223: 4, 27, 39, 65, 81
    224: 4, 27, 51, 63, 98
    225: 4, 27, 51, 68, 93
    226: 4, 27, 51, 86, 93
    227: 4, 27, 56, 81, 93
    228: 4, 27, 58, 63, 91
    229: 4, 27, 63, 81, 95
    230: 4, 27, 63, 85, 91
    231: 4, 27, 65, 81, 93
    232: 4, 28, 35, 76, 91
    233: 4, 28, 36, 57, 91
    234: 4, 28, 36, 75, 91
    235: 4, 28, 39, 51, 76
    236: 4, 28, 51, 76, 93
    237: 4, 28, 57, 63, 91
    238: 4, 28, 63, 75, 91
    239: 4, 32, 51, 69, 78
    240: 4, 32, 51, 69, 87
    241: 4, 32, 51, 76, 98
    242: 4, 32, 51, 78, 96
    243: 4, 32, 51, 87, 96
    244: 4, 32, 56, 78, 91
    245: 4, 32, 56, 87, 91
    246: 4, 32, 57, 68, 91
    247: 4, 32, 57, 69, 81
    248: 4, 32, 57, 81, 96
    249: 4, 32, 57, 86, 91
    250: 4, 32, 58, 76, 91
    251: 4, 32, 65, 78, 91
    252: 4, 32, 65, 87, 91
    253: 4, 32, 68, 75, 91
    254: 4, 32, 69, 75, 81
    255: 4, 32, 75, 81, 96
    256: 4, 32, 75, 86, 91
    257: 4, 32, 76, 81, 95
    258: 4, 32, 76, 85, 91
    259: 4, 35, 62, 78, 91
    260: 4, 35, 62, 87, 91
    261: 4, 35, 68, 72, 91
    262: 4, 35, 69, 72, 81
    263: 4, 35, 72, 81, 96
    264: 4, 35, 72, 86, 91
    265: 4, 35, 76, 81, 92
    266: 4, 35, 76, 82, 91
    267: 4, 36, 51, 72, 98
    268: 4, 36, 51, 78, 92
    269: 4, 36, 51, 87, 92
    270: 4, 36, 52, 78, 91
    271: 4, 36, 52, 87, 91
    272: 4, 36, 57, 81, 92
    273: 4, 36, 57, 82, 91
    274: 4, 36, 58, 72, 91
    275: 4, 36, 72, 81, 95
    276: 4, 36, 72, 85, 91
    277: 4, 36, 75, 81, 92
    278: 4, 36, 75, 82, 91
    279: 4, 38, 51, 69, 72
    280: 4, 38, 51, 72, 96
    281: 4, 38, 51, 76, 92
    282: 4, 38, 52, 76, 91
    283: 4, 38, 56, 72, 91
    284: 4, 38, 57, 62, 91
    285: 4, 38, 62, 75, 91
    286: 4, 38, 65, 72, 91
    287: 4, 39, 51, 62, 78
    288: 4, 39, 51, 62, 87
    289: 4, 39, 51, 68, 72
    290: 4, 39, 51, 72, 86
    291: 4, 39, 51, 76, 82
    292: 4, 39, 52, 76, 81
    293: 4, 39, 56, 72, 81
    294: 4, 39, 57, 62, 81
    295: 4, 39, 62, 75, 81
    296: 4, 39, 65, 72, 81
    297: 4, 51, 62, 78, 93
    298: 4, 51, 62, 87, 93
    299: 4, 51, 63, 72, 98
    300: 4, 51, 63, 78, 92
    301: 4, 51, 63, 87, 92
    302: 4, 51, 68, 72, 93
    303: 4, 51, 72, 86, 93
    304: 4, 51, 76, 82, 93
    305: 4, 52, 63, 78, 91
    306: 4, 52, 63, 87, 91
    307: 4, 52, 76, 81, 93
    308: 4, 56, 72, 81, 93
    309: 4, 57, 62, 81, 93
    310: 4, 57, 63, 81, 92
    311: 4, 57, 63, 82, 91
    312: 4, 58, 63, 72, 91
    313: 4, 62, 75, 81, 93
    314: 4, 63, 72, 81, 95
    315: 4, 63, 72, 85, 91
    316: 4, 63, 75, 81, 92
    317: 4, 63, 75, 82, 91
    318: 4, 65, 72, 81, 93
    319: 6, 12, 34, 57, 98
    320: 6, 12, 34, 75, 98
    321: 6, 12, 34, 78, 95
    322: 6, 12, 34, 87, 95
    323: 6, 12, 35, 49, 78
    324: 6, 12, 35, 49, 87
    325: 6, 12, 35, 74, 98
    326: 6, 12, 35, 78, 94
    327: 6, 12, 35, 87, 94
    328: 6, 12, 38, 49, 57
    329: 6, 12, 38, 49, 75
    330: 6, 12, 38, 57, 94
    331: 6, 12, 38, 74, 95
    332: 6, 12, 38, 75, 94
    333: 6, 12, 39, 45, 78
    334: 6, 12, 39, 45, 87
    335: 6, 12, 39, 48, 57
    336: 6, 12, 39, 48, 75
    337: 6, 12, 39, 54, 78
    338: 6, 12, 39, 54, 87
    339: 6, 12, 39, 57, 84
    340: 6, 12, 39, 58, 74
    341: 6, 12, 39, 74, 85
    342: 6, 12, 39, 75, 84
    343: 6, 12, 45, 78, 93
    344: 6, 12, 45, 87, 93
    345: 6, 12, 48, 57, 93
    346: 6, 12, 48, 75, 93
    347: 6, 12, 54, 78, 93
    348: 6, 12, 54, 87, 93
    349: 6, 12, 57, 84, 93
    350: 6, 12, 58, 74, 93
    351: 6, 12, 74, 85, 93
    352: 6, 12, 75, 84, 93
    353: 6, 14, 25, 39, 78
    354: 6, 14, 25, 39, 87
    355: 6, 14, 25, 78, 93
    356: 6, 14, 25, 87, 93
    357: 6, 14, 27, 35, 98
    358: 6, 14, 27, 38, 95
    359: 6, 14, 27, 39, 58
    360: 6, 14, 27, 39, 85
    361: 6, 14, 27, 58, 93
    362: 6, 14, 27, 85, 93
    363: 6, 14, 28, 39, 57
    364: 6, 14, 28, 39, 75
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    366: 6, 14, 28, 75, 93
    367: 6, 14, 32, 57, 98
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    369: 6, 14, 32, 78, 95
    370: 6, 14, 32, 87, 95
    371: 6, 14, 35, 72, 98
    372: 6, 14, 35, 78, 92
    373: 6, 14, 35, 87, 92
    374: 6, 14, 38, 57, 92
    375: 6, 14, 38, 72, 95
    376: 6, 14, 38, 75, 92
    377: 6, 14, 39, 52, 78
    378: 6, 14, 39, 52, 87
    379: 6, 14, 39, 57, 82
    380: 6, 14, 39, 58, 72
    381: 6, 14, 39, 72, 85
    382: 6, 14, 39, 75, 82
    383: 6, 14, 52, 78, 93
    384: 6, 14, 52, 87, 93
    385: 6, 14, 57, 82, 93
    386: 6, 14, 58, 72, 93
    387: 6, 14, 72, 85, 93
    388: 6, 14, 75, 82, 93
    389: 6, 15, 24, 39, 78
    390: 6, 15, 24, 39, 87
    391: 6, 15, 24, 78, 93
    392: 6, 15, 24, 87, 93
    393: 6, 15, 27, 34, 98
    394: 6, 15, 27, 38, 49
    395: 6, 15, 27, 38, 94
    396: 6, 15, 27, 39, 48
    397: 6, 15, 27, 39, 84
    398: 6, 15, 27, 48, 93
    399: 6, 15, 27, 84, 93
    400: 6, 15, 28, 39, 74
    401: 6, 15, 28, 74, 93
    402: 6, 15, 32, 49, 78
    403: 6, 15, 32, 49, 87
    404: 6, 15, 32, 74, 98
    405: 6, 15, 32, 78, 94
    406: 6, 15, 32, 87, 94
    407: 6, 15, 34, 72, 98
    408: 6, 15, 34, 78, 92
    409: 6, 15, 34, 87, 92
    410: 6, 15, 38, 49, 72
    411: 6, 15, 38, 72, 94
    412: 6, 15, 38, 74, 92
    413: 6, 15, 39, 42, 78
    414: 6, 15, 39, 42, 87
    415: 6, 15, 39, 48, 72
    416: 6, 15, 39, 72, 84
    417: 6, 15, 39, 74, 82
    418: 6, 15, 42, 78, 93
    419: 6, 15, 42, 87, 93
    420: 6, 15, 48, 72, 93
    421: 6, 15, 72, 84, 93
    422: 6, 15, 74, 82, 93
    423: 6, 18, 24, 39, 57
    424: 6, 18, 24, 39, 75
    425: 6, 18, 24, 57, 93
    426: 6, 18, 24, 75, 93
    427: 6, 18, 25, 39, 74
    428: 6, 18, 25, 74, 93
    429: 6, 18, 27, 34, 95
    430: 6, 18, 27, 35, 49
    431: 6, 18, 27, 35, 94
    432: 6, 18, 27, 39, 45
    433: 6, 18, 27, 39, 54
    434: 6, 18, 27, 45, 93
    435: 6, 18, 27, 54, 93
    436: 6, 18, 32, 49, 57
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    1010: 9, 16, 25, 34, 87
    1011: 9, 16, 25, 38, 74
    1012: 9, 16, 27, 34, 58
    1013: 9, 16, 27, 34, 85
    1014: 9, 16, 27, 35, 48
    1015: 9, 16, 27, 35, 84
    1016: 9, 16, 27, 38, 45
    1017: 9, 16, 27, 38, 54
    1018: 9, 16, 28, 34, 57
    1019: 9, 16, 28, 34, 75
    1020: 9, 16, 28, 35, 74
    1021: 9, 16, 32, 45, 78
    1022: 9, 16, 32, 45, 87
    1023: 9, 16, 32, 48, 57
    1024: 9, 16, 32, 48, 75
    1025: 9, 16, 32, 54, 78
    1026: 9, 16, 32, 54, 87
    1027: 9, 16, 32, 57, 84
    1028: 9, 16, 32, 58, 74
    1029: 9, 16, 32, 74, 85
    1030: 9, 16, 32, 75, 84
    1031: 9, 16, 34, 52, 78
    1032: 9, 16, 34, 52, 87
    1033: 9, 16, 34, 57, 82
    1034: 9, 16, 34, 58, 72
    1035: 9, 16, 34, 72, 85
    1036: 9, 16, 34, 75, 82
    1037: 9, 16, 35, 42, 78
    1038: 9, 16, 35, 42, 87
    1039: 9, 16, 35, 48, 72
    1040: 9, 16, 35, 72, 84
    1041: 9, 16, 35, 74, 82
    1042: 9, 16, 38, 42, 57
    1043: 9, 16, 38, 42, 75
    1044: 9, 16, 38, 45, 72
    1045: 9, 16, 38, 52, 74
    1046: 9, 16, 38, 54, 72
    1047: 9, 18, 24, 35, 76
    1048: 9, 18, 24, 36, 57
    1049: 9, 18, 24, 36, 75
    1050: 9, 18, 24, 57, 63
    1051: 9, 18, 24, 63, 75
    1052: 9, 18, 25, 34, 76
    1053: 9, 18, 25, 36, 74
    1054: 9, 18, 25, 63, 74
    1055: 9, 18, 26, 34, 57
    1056: 9, 18, 26, 34, 75
    1057: 9, 18, 26, 35, 74
    1058: 9, 18, 27, 34, 56
    1059: 9, 18, 27, 34, 65
    1060: 9, 18, 27, 35, 46
    1061: 9, 18, 27, 35, 64
    1062: 9, 18, 27, 36, 45
    1063: 9, 18, 27, 36, 54
    1064: 9, 18, 27, 45, 63
    1065: 9, 18, 27, 54, 63
    1066: 9, 18, 32, 45, 76
    1067: 9, 18, 32, 46, 57
    1068: 9, 18, 32, 46, 75
    1069: 9, 18, 32, 54, 76
    1070: 9, 18, 32, 56, 74
    1071: 9, 18, 32, 57, 64
    1072: 9, 18, 32, 64, 75
    1073: 9, 18, 32, 65, 74
    1074: 9, 18, 34, 52, 76
    1075: 9, 18, 34, 56, 72
    1076: 9, 18, 34, 57, 62
    1077: 9, 18, 34, 62, 75
    1078: 9, 18, 34, 65, 72
    1079: 9, 18, 35, 42, 76
    1080: 9, 18, 35, 46, 72
    1081: 9, 18, 35, 62, 74
    1082: 9, 18, 35, 64, 72
    1083: 9, 18, 36, 42, 57
    1084: 9, 18, 36, 42, 75
    1085: 9, 18, 36, 45, 72
    1086: 9, 18, 36, 52, 74
    1087: 9, 18, 36, 54, 72
    1088: 9, 18, 42, 57, 63
    1089: 9, 18, 42, 63, 75
    1090: 9, 18, 45, 63, 72
    1091: 9, 18, 52, 63, 74
    1092: 9, 18, 54, 63, 72
    1093: 9, 21, 34, 56, 78
    1094: 9, 21, 34, 56, 87
    1095: 9, 21, 34, 57, 68
    1096: 9, 21, 34, 57, 86
    1097: 9, 21, 34, 58, 76
    1098: 9, 21, 34, 65, 78
    1099: 9, 21, 34, 65, 87
    1100: 9, 21, 34, 68, 75
    1101: 9, 21, 34, 75, 86
    1102: 9, 21, 34, 76, 85
    1103: 9, 21, 35, 46, 78
    1104: 9, 21, 35, 46, 87
    1105: 9, 21, 35, 48, 76
    1106: 9, 21, 35, 64, 78
    1107: 9, 21, 35, 64, 87
    1108: 9, 21, 35, 68, 74
    1109: 9, 21, 35, 74, 86
    1110: 9, 21, 35, 76, 84
    1111: 9, 21, 36, 45, 78
    1112: 9, 21, 36, 45, 87
    1113: 9, 21, 36, 48, 57
    1114: 9, 21, 36, 48, 75
    1115: 9, 21, 36, 54, 78
    1116: 9, 21, 36, 54, 87
    1117: 9, 21, 36, 57, 84
    1118: 9, 21, 36, 58, 74
    1119: 9, 21, 36, 74, 85
    1120: 9, 21, 36, 75, 84
    1121: 9, 21, 38, 45, 76
    1122: 9, 21, 38, 46, 57
    1123: 9, 21, 38, 46, 75
    1124: 9, 21, 38, 54, 76
    1125: 9, 21, 38, 56, 74
    1126: 9, 21, 38, 57, 64
    1127: 9, 21, 38, 64, 75
    1128: 9, 21, 38, 65, 74
    1129: 9, 21, 45, 63, 78
    1130: 9, 21, 45, 63, 87
    1131: 9, 21, 48, 57, 63
    1132: 9, 21, 48, 63, 75
    1133: 9, 21, 54, 63, 78
    1134: 9, 21, 54, 63, 87
    1135: 9, 21, 57, 63, 84
    1136: 9, 21, 58, 63, 74
    1137: 9, 21, 63, 74, 85
    1138: 9, 21, 63, 75, 84
    1139: 9, 24, 35, 76, 81
    1140: 9, 24, 36, 51, 78
    1141: 9, 24, 36, 51, 87
    1142: 9, 24, 36, 57, 81
    1143: 9, 24, 36, 75, 81
    1144: 9, 24, 38, 51, 76
    1145: 9, 24, 51, 63, 78
    1146: 9, 24, 51, 63, 87
    1147: 9, 24, 57, 63, 81
    1148: 9, 24, 63, 75, 81
    1149: 9, 25, 34, 76, 81
    1150: 9, 25, 36, 74, 81
    1151: 9, 25, 63, 74, 81
    1152: 9, 26, 34, 51, 78
    1153: 9, 26, 34, 51, 87
    1154: 9, 26, 34, 57, 81
    1155: 9, 26, 34, 75, 81
    1156: 9, 26, 35, 74, 81
    1157: 9, 26, 38, 51, 74
    1158: 9, 27, 34, 51, 68
    1159: 9, 27, 34, 51, 86
    1160: 9, 27, 34, 56, 81
    1161: 9, 27, 34, 65, 81
    1162: 9, 27, 35, 46, 81
    1163: 9, 27, 35, 64, 81
    1164: 9, 27, 36, 45, 81
    1165: 9, 27, 36, 48, 51
    1166: 9, 27, 36, 51, 84
    1167: 9, 27, 36, 54, 81
    1168: 9, 27, 38, 46, 51
    1169: 9, 27, 38, 51, 64
    1170: 9, 27, 45, 63, 81
    1171: 9, 27, 48, 51, 63
    1172: 9, 27, 51, 63, 84
    1173: 9, 27, 54, 63, 81
    1174: 9, 28, 34, 51, 76
    1175: 9, 28, 36, 51, 74
    1176: 9, 28, 51, 63, 74
    1177: 9, 32, 45, 76, 81
    1178: 9, 32, 46, 51, 78
    1179: 9, 32, 46, 51, 87
    1180: 9, 32, 46, 57, 81
    1181: 9, 32, 46, 75, 81
    1182: 9, 32, 48, 51, 76
    1183: 9, 32, 51, 64, 78
    1184: 9, 32, 51, 64, 87
    1185: 9, 32, 51, 68, 74
    1186: 9, 32, 51, 74, 86
    1187: 9, 32, 51, 76, 84
    1188: 9, 32, 54, 76, 81
    1189: 9, 32, 56, 74, 81
    1190: 9, 32, 57, 64, 81
    1191: 9, 32, 64, 75, 81
    1192: 9, 32, 65, 74, 81
    1193: 9, 34, 51, 62, 78
    1194: 9, 34, 51, 62, 87
    1195: 9, 34, 51, 68, 72
    1196: 9, 34, 51, 72, 86
    1197: 9, 34, 51, 76, 82
    1198: 9, 34, 52, 76, 81
    1199: 9, 34, 56, 72, 81
    1200: 9, 34, 57, 62, 81
    1201: 9, 34, 62, 75, 81
    1202: 9, 34, 65, 72, 81
    1203: 9, 35, 42, 76, 81
    1204: 9, 35, 46, 72, 81
    1205: 9, 35, 62, 74, 81
    1206: 9, 35, 64, 72, 81
    1207: 9, 36, 42, 51, 78
    1208: 9, 36, 42, 51, 87
    1209: 9, 36, 42, 57, 81
    1210: 9, 36, 42, 75, 81
    1211: 9, 36, 45, 72, 81
    1212: 9, 36, 48, 51, 72
    1213: 9, 36, 51, 72, 84
    1214: 9, 36, 51, 74, 82
    1215: 9, 36, 52, 74, 81
    1216: 9, 36, 54, 72, 81
    1217: 9, 38, 42, 51, 76
    1218: 9, 38, 46, 51, 72
    1219: 9, 38, 51, 62, 74
    1220: 9, 38, 51, 64, 72
    1221: 9, 42, 51, 63, 78
    1222: 9, 42, 51, 63, 87
    1223: 9, 42, 57, 63, 81
    1224: 9, 42, 63, 75, 81
    1225: 9, 45, 63, 72, 81
    1226: 9, 48, 51, 63, 72
    1227: 9, 51, 63, 72, 84
    1228: 9, 51, 63, 74, 82
    1229: 9, 52, 63, 74, 81
    1230: 9, 54, 63, 72, 81

  12. Alex, Nadav, Evan, Miles got:
    2/8, 3/7=6/14, and 9/5. We feel that the intervals are more accurate than some of the answers above.

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