Open Middle®
Directions: Using the digits 0 to 9, at most one time each, place a digit in each box to make the statement true.
Hint
How can you choose digits for your addends so that the sum is a double digit number?
Answer
There are 286 unique solutions. Three examples are:
1: 0 x 1 + 4 x 8 = 32
2: 0 x 1 + 8 x 3 = 24
3: 0 x 1 + 8 x 7 = 56
1: 0 x 1 + 4 x 8 = 32
2: 0 x 1 + 8 x 3 = 24
3: 0 x 1 + 8 x 7 = 56
Source: Owen Kaplinsky
wouldn’t 8 times 7 plus 2 times 10 equals 76 me true
I don’t think so, because you are only allowed to use the digits once, and in this case the 7 is used twice.
A ‘box’ can only contain one digit, so 10 is not an option.
( 3×2)+(7×7)=53
It would be 6×8 + 4×5 = 88
(2×2)+(8×8)=68
(7×6) + (2×3)= 48
But isn’t that the same thing as 7×6+3×2 which is on the list
5×6 + 4×2 = 38
(3*9)+(5*0)=27
(4*6)+(8*9)=96
It would be 6×8 + 4×5 = 88
(3×3) + (4×5)=29
2*5+7*4=38
(7×9)+(1×0)=63
(1 x2) + (4 x 4) = 18
(5 x 8) + (2 x 6) = 52
4×6 + 8×9= 96
3*9+5*0=27
4*0+ 7*3 = 21
16+6=22
8*2=16+6=22
8 x 3 + 8 x 3 = 48
(3×4)+(6×2)=24
0x1+4×8=32
1×2 + 3×4 = 14
1 x 4 + 0 x 7 = 4
2 x 3 + 4 x 5 = 26.
Sometimes, this may result in three digit numbers.
9 x 8 + 7 x 6 =114
9 x 2 + 3 x 0 = 18
ok so my equation is
(9×5)+(3×4)=67
My equation is (3×4)+(5×7)=47
My equation is
(3×6)+(5+7)=
53!!!!
I wonder why they missed them. Or are they wrong? I don’t think so though
Yes there are wrong to ∞ and beyond
1×1+1,000,000,000,000=1,000,000,000,001
( 9 x 9 )+( 9 x 0 ) = 81
(6×3) + (9×7) = 81
1: 0 x 1 + 4 x 8 = 32
2: 0 x 1 + 8 x 3 = 24
3: 0 x 1 + 8 x 7 = 56
4: 0 x 1 + 9 x 6 = 54
5: 0 x 1 + 9 x 8 = 72
6: 0 x 2 + 7 x 9 = 63
7: 0 x 3 + 2 x 7 = 14
8: 0 x 3 + 4 x 7 = 28
9: 0 x 3 + 7 x 6 = 42
10: 0 x 3 + 8 x 2 = 16
11: 0 x 3 + 9 x 6 = 54
12: 0 x 4 + 3 x 9 = 27
13: 0 x 4 + 7 x 8 = 56
14: 0 x 4 + 7 x 9 = 63
15: 0 x 5 + 2 x 7 = 14
16: 0 x 5 + 4 x 7 = 28
17: 0 x 5 + 4 x 9 = 36
18: 0 x 5 + 6 x 3 = 18
19: 0 x 5 + 7 x 3 = 21
20: 0 x 5 + 8 x 4 = 32
21: 0 x 5 + 8 x 9 = 72
22: 0 x 5 + 9 x 7 = 63
23: 0 x 6 + 3 x 4 = 12
24: 0 x 6 + 4 x 7 = 28
25: 0 x 6 + 7 x 2 = 14
26: 0 x 6 + 9 x 2 = 18
27: 0 x 7 + 2 x 8 = 16
28: 0 x 7 + 3 x 6 = 18
29: 0 x 7 + 6 x 9 = 54
30: 0 x 7 + 9 x 2 = 18
31: 0 x 8 + 4 x 3 = 12
32: 0 x 8 + 6 x 7 = 42
33: 0 x 8 + 7 x 3 = 21
34: 0 x 9 + 3 x 7 = 21
35: 0 x 9 + 4 x 3 = 12
36: 0 x 9 + 4 x 7 = 28
37: 0 x 9 + 7 x 2 = 14
38: 0 x 9 + 7 x 6 = 42
39: 0 x 9 + 8 x 2 = 16
40: 0 x 9 + 8 x 4 = 32
41: 1 x 0 + 4 x 7 = 28
42: 1 x 0 + 7 x 6 = 42
43: 1 x 0 + 9 x 3 = 27
44: 1 x 0 + 9 x 4 = 36
45: 1 x 0 + 9 x 7 = 63
46: 1 x 2 + 7 x 9 = 65
47: 1 x 2 + 9 x 4 = 38
48: 1 x 3 + 9 x 6 = 57
49: 1 x 3 + 9 x 8 = 75
50: 1 x 4 + 3 x 7 = 25
51: 1 x 4 + 6 x 8 = 52
52: 1 x 4 + 6 x 9 = 58
53: 1 x 5 + 3 x 7 = 26
54: 1 x 7 + 3 x 6 = 25
55: 1 x 8 + 3 x 4 = 20
56: 1 x 8 + 5 x 7 = 43
57: 1 x 8 + 6 x 7 = 50
58: 1 x 9 + 7 x 8 = 65
59: 1 x 9 + 8 x 6 = 57
60: 2 x 0 + 3 x 6 = 18
61: 2 x 0 + 4 x 9 = 36
62: 2 x 0 + 6 x 9 = 54
63: 2 x 0 + 7 x 8 = 56
64: 2 x 1 + 4 x 7 = 30
65: 2 x 1 + 8 x 6 = 50
66: 2 x 1 + 9 x 5 = 47
67: 2 x 1 + 9 x 8 = 74
68: 2 x 3 + 6 x 7 = 48
69: 2 x 3 + 7 x 5 = 41
70: 2 x 4 + 6 x 5 = 38
71: 2 x 4 + 6 x 7 = 50
72: 2 x 5 + 7 x 4 = 38
73: 2 x 7 + 0 x 5 = 14
74: 2 x 7 + 0 x 9 = 14
75: 2 x 7 + 4 x 6 = 38
76: 2 x 8 + 5 x 0 = 16
77: 2 x 9 + 0 x 7 = 18
78: 2 x 9 + 5 x 4 = 38
79: 2 x 9 + 5 x 6 = 48
80: 2 x 9 + 6 x 0 = 18
81: 2 x 9 + 8 x 4 = 50
82: 3 x 0 + 2 x 9 = 18
83: 3 x 0 + 7 x 8 = 56
84: 3 x 0 + 9 x 8 = 72
85: 3 x 1 + 4 x 6 = 27
86: 3 x 1 + 6 x 7 = 45
87: 3 x 1 + 8 x 7 = 59
88: 3 x 1 + 9 x 5 = 48
89: 3 x 2 + 6 x 8 = 54
90: 3 x 2 + 8 x 5 = 46
91: 3 x 4 + 0 x 5 = 12
92: 3 x 4 + 0 x 9 = 12
93: 3 x 4 + 6 x 0 = 12
94: 3 x 4 + 7 x 0 = 12
95: 3 x 6 + 0 x 5 = 18
96: 3 x 6 + 0 x 7 = 18
97: 3 x 6 + 1 x 7 = 25
98: 3 x 6 + 4 x 0 = 18
99: 3 x 6 + 4 x 8 = 50
100: 3 x 7 + 1 x 4 = 25
101: 3 x 7 + 1 x 5 = 26
102: 3 x 7 + 8 x 0 = 21
103: 3 x 7 + 8 x 5 = 61
104: 3 x 7 + 9 x 0 = 21
105: 3 x 8 + 0 x 6 = 24
106: 3 x 8 + 1 x 0 = 24
107: 3 x 8 + 9 x 0 = 24
108: 3 x 8 + 9 x 4 = 60
109: 3 x 9 + 0 x 6 = 27
110: 3 x 9 + 2 x 7 = 41
111: 3 x 9 + 5 x 7 = 62
112: 4 x 0 + 2 x 8 = 16
113: 4 x 0 + 3 x 6 = 18
114: 4 x 0 + 7 x 3 = 21
115: 4 x 0 + 8 x 9 = 72
116: 4 x 0 + 9 x 2 = 18
117: 4 x 1 + 5 x 7 = 39
118: 4 x 1 + 8 x 7 = 60
119: 4 x 1 + 9 x 8 = 76
120: 4 x 3 + 0 x 8 = 12
121: 4 x 3 + 8 x 1 = 20
122: 4 x 5 + 2 x 8 = 36
123: 4 x 5 + 7 x 9 = 83
124: 4 x 6 + 2 x 7 = 38
125: 4 x 6 + 8 x 1 = 32
126: 4 x 6 + 9 x 3 = 51
127: 4 x 7 + 0 x 3 = 28
128: 4 x 7 + 0 x 6 = 28
129: 4 x 7 + 1 x 0 = 28
130: 4 x 7 + 8 x 1 = 36
131: 4 x 7 + 8 x 3 = 52
132: 4 x 8 + 0 x 1 = 32
133: 4 x 8 + 0 x 5 = 32
134: 4 x 8 + 0 x 7 = 32
135: 4 x 8 + 1 x 7 = 39
136: 4 x 8 + 9 x 2 = 50
137: 4 x 9 + 0 x 5 = 36
138: 4 x 9 + 0 x 7 = 36
139: 4 x 9 + 2 x 1 = 38
140: 4 x 9 + 2 x 7 = 50
141: 4 x 9 + 5 x 8 = 76
142: 4 x 9 + 8 x 0 = 36
143: 4 x 9 + 8 x 3 = 60
144: 5 x 0 + 2 x 8 = 16
145: 5 x 0 + 3 x 8 = 24
146: 5 x 0 + 3 x 9 = 27
147: 5 x 0 + 4 x 3 = 12
148: 5 x 0 + 7 x 6 = 42
149: 5 x 0 + 9 x 2 = 18
150: 5 x 1 + 4 x 6 = 29
151: 5 x 1 + 4 x 8 = 37
152: 5 x 1 + 8 x 3 = 29
153: 5 x 1 + 9 x 7 = 68
154: 5 x 3 + 1 x 9 = 24
155: 5 x 4 + 9 x 2 = 38
156: 5 x 6 + 4 x 2 = 38
157: 5 x 7 + 1 x 4 = 39
158: 5 x 7 + 3 x 9 = 62
159: 5 x 8 + 3 x 7 = 61
160: 5 x 8 + 9 x 4 = 76
161: 6 x 0 + 3 x 7 = 21
162: 6 x 0 + 4 x 8 = 32
163: 6 x 0 + 8 x 3 = 24
164: 6 x 0 + 8 x 9 = 72
165: 6 x 0 + 9 x 3 = 27
166: 6 x 3 + 0 x 2 = 18
167: 6 x 3 + 9 x 0 = 18
168: 6 x 3 + 9 x 1 = 27
169: 6 x 3 + 9 x 7 = 81
170: 6 x 4 + 3 x 1 = 27
171: 6 x 4 + 5 x 1 = 29
172: 6 x 5 + 9 x 2 = 48
173: 6 x 7 + 0 x 3 = 42
174: 6 x 7 + 1 x 0 = 42
175: 6 x 7 + 5 x 0 = 42
176: 6 x 7 + 8 x 1 = 50
177: 6 x 7 + 9 x 0 = 42
178: 6 x 9 + 0 x 7 = 54
179: 6 x 9 + 0 x 8 = 54
180: 6 x 9 + 2 x 0 = 54
181: 7 x 0 + 4 x 3 = 12
182: 7 x 0 + 4 x 9 = 36
183: 7 x 0 + 8 x 3 = 24
184: 7 x 0 + 8 x 4 = 32
185: 7 x 1 + 8 x 4 = 39
186: 7 x 2 + 0 x 6 = 14
187: 7 x 2 + 0 x 8 = 14
188: 7 x 2 + 3 x 0 = 14
189: 7 x 2 + 3 x 9 = 41
190: 7 x 2 + 4 x 9 = 50
191: 7 x 3 + 0 x 5 = 21
192: 7 x 3 + 0 x 6 = 21
193: 7 x 3 + 4 x 0 = 21
194: 7 x 3 + 8 x 1 = 29
195: 7 x 4 + 0 x 9 = 28
196: 7 x 4 + 2 x 1 = 30
197: 7 x 4 + 2 x 5 = 38
198: 7 x 4 + 5 x 0 = 28
199: 7 x 4 + 6 x 9 = 82
200: 7 x 5 + 2 x 3 = 41
201: 7 x 5 + 8 x 1 = 43
202: 7 x 6 + 0 x 8 = 42
203: 7 x 6 + 3 x 1 = 45
204: 7 x 6 + 3 x 2 = 48
205: 7 x 6 + 4 x 2 = 50
206: 7 x 8 + 0 x 3 = 56
207: 7 x 8 + 0 x 9 = 56
208: 7 x 8 + 2 x 0 = 56
209: 7 x 8 + 3 x 1 = 59
210: 7 x 8 + 4 x 0 = 56
211: 7 x 9 + 1 x 5 = 68
212: 7 x 9 + 2 x 0 = 63
213: 7 x 9 + 4 x 5 = 83
214: 8 x 0 + 6 x 9 = 54
215: 8 x 0 + 7 x 2 = 14
216: 8 x 0 + 7 x 9 = 63
217: 8 x 0 + 9 x 3 = 27
218: 8 x 0 + 9 x 4 = 36
219: 8 x 1 + 3 x 7 = 29
220: 8 x 1 + 6 x 4 = 32
221: 8 x 1 + 7 x 4 = 36
222: 8 x 2 + 0 x 4 = 16
223: 8 x 2 + 0 x 7 = 16
224: 8 x 2 + 3 x 0 = 16
225: 8 x 2 + 4 x 5 = 36
226: 8 x 2 + 6 x 9 = 70
227: 8 x 2 + 9 x 0 = 16
228: 8 x 2 + 9 x 5 = 61
229: 8 x 3 + 0 x 5 = 24
230: 8 x 3 + 5 x 1 = 29
231: 8 x 3 + 7 x 0 = 24
232: 8 x 3 + 7 x 4 = 52
233: 8 x 4 + 0 x 9 = 32
234: 8 x 4 + 1 x 5 = 37
235: 8 x 4 + 3 x 6 = 50
236: 8 x 4 + 6 x 0 = 32
237: 8 x 5 + 2 x 3 = 46
238: 8 x 5 + 3 x 9 = 67
239: 8 x 6 + 1 x 2 = 50
240: 8 x 6 + 3 x 2 = 54
241: 8 x 6 + 3 x 9 = 75
242: 8 x 6 + 4 x 1 = 52
243: 8 x 6 + 9 x 1 = 57
244: 8 x 7 + 0 x 1 = 56
245: 8 x 7 + 1 x 9 = 65
246: 8 x 7 + 4 x 1 = 60
247: 8 x 9 + 0 x 5 = 72
248: 8 x 9 + 1 x 0 = 72
249: 8 x 9 + 1 x 2 = 74
250: 8 x 9 + 1 x 3 = 75
251: 8 x 9 + 4 x 0 = 72
252: 9 x 0 + 3 x 8 = 24
253: 9 x 0 + 6 x 3 = 18
254: 9 x 0 + 7 x 8 = 56
255: 9 x 1 + 3 x 5 = 24
256: 9 x 1 + 3 x 6 = 27
257: 9 x 2 + 0 x 4 = 18
258: 9 x 2 + 0 x 5 = 18
259: 9 x 2 + 3 x 0 = 18
260: 9 x 3 + 0 x 5 = 27
261: 9 x 3 + 0 x 8 = 27
262: 9 x 3 + 1 x 0 = 27
263: 9 x 3 + 4 x 0 = 27
264: 9 x 3 + 5 x 8 = 67
265: 9 x 3 + 6 x 4 = 51
266: 9 x 3 + 6 x 8 = 75
267: 9 x 4 + 1 x 0 = 36
268: 9 x 4 + 2 x 0 = 36
269: 9 x 5 + 2 x 1 = 47
270: 9 x 5 + 3 x 1 = 48
271: 9 x 5 + 8 x 2 = 61
272: 9 x 6 + 0 x 1 = 54
273: 9 x 6 + 0 x 3 = 54
274: 9 x 6 + 1 x 3 = 57
275: 9 x 6 + 1 x 4 = 58
276: 9 x 6 + 2 x 8 = 70
277: 9 x 6 + 7 x 4 = 82
278: 9 x 7 + 0 x 1 = 63
279: 9 x 7 + 0 x 8 = 63
280: 9 x 7 + 2 x 1 = 65
281: 9 x 7 + 4 x 0 = 63
282: 9 x 7 + 5 x 0 = 63
283: 9 x 7 + 6 x 3 = 81
284: 9 x 8 + 3 x 0 = 72
285: 9 x 8 + 4 x 1 = 76
286: 9 x 8 + 6 x 0 = 72