# Coordinate Parallelograms

Directions: Using the digits 1 to 9 at most one time each, fill in the boxes so that the points make a parallelogram.

### Hint

What do you know about a parallelogram that would help you with this problem? Which points need to be connected to make parallel sides?

Number of Unique Solutions: 696
1: (1,2),(3,5),(6,4),(8,7)
2: (1,2),(3,6),(7,4),(9,8)
3: (1,2),(4,3),(6,7),(9,8)
4: (1,2),(4,7),(6,3),(9,8)
5: (1,3),(2,4),(8,5),(9,6)
6: (1,3),(2,8),(5,4),(6,9)
7: (1,3),(4,7),(5,2),(8,6)
8: (1,3),(5,7),(4,2),(8,6)
9: (1,3),(7,4),(2,5),(8,6)
10: (1,3),(8,4),(2,5),(9,6)
11: (1,3),(8,6),(2,4),(9,7)
12: (1,4),(2,3),(8,6),(9,5)
13: (1,4),(2,6),(8,3),(9,5)
14: (1,4),(2,6),(8,5),(9,7)
15: (1,4),(2,9),(5,3),(6,8)
16: (1,4),(3,7),(6,2),(8,5)
17: (1,4),(5,8),(2,3),(6,7)
18: (1,4),(5,8),(3,2),(7,6)
19: (1,4),(5,9),(2,3),(6,8)
20: (1,4),(6,5),(2,8),(7,9)
21: (1,4),(6,9),(2,3),(7,8)
22: (1,5),(2,3),(8,6),(9,4)
23: (1,5),(2,6),(7,3),(8,4)
24: (1,5),(3,2),(6,7),(8,4)
25: (1,5),(3,6),(2,8),(4,9)
26: (1,5),(6,4),(2,9),(7,8)
27: (1,5),(7,6),(2,3),(8,4)
28: (1,5),(8,7),(2,4),(9,6)
29: (1,6),(2,4),(7,5),(8,3)
30: (1,6),(2,5),(3,9),(4,8)
31: (1,6),(2,5),(7,4),(8,3)
32: (1,6),(2,5),(8,4),(9,3)
33: (1,6),(2,7),(4,8),(5,9)
34: (1,6),(2,9),(3,5),(4,8)
35: (1,6),(3,2),(7,8),(9,4)
36: (1,6),(8,3),(2,7),(9,4)
37: (1,6),(8,5),(2,4),(9,3)
38: (1,6),(8,7),(2,4),(9,5)
39: (1,7),(2,8),(3,5),(4,6)
40: (1,7),(2,9),(3,6),(4,8)
41: (1,7),(3,8),(2,5),(4,6)
42: (1,7),(4,3),(5,6),(8,2)
43: (1,7),(4,6),(2,9),(5,8)
44: (1,7),(5,8),(2,3),(6,4)
45: (1,7),(6,2),(4,8),(9,3)
46: (1,7),(6,4),(3,5),(8,2)
47: (1,8),(2,4),(5,7),(6,3)
48: (1,8),(2,9),(3,6),(4,7)
49: (1,8),(2,9),(4,6),(5,7)
50: (1,8),(3,4),(7,6),(9,2)
51: (1,8),(3,6),(7,4),(9,2)
52: (1,8),(5,9),(2,3),(6,4)
53: (1,8),(6,9),(2,4),(7,5)
54: (1,9),(2,5),(6,8),(7,4)
55: (1,9),(3,8),(2,7),(4,6)
56: (1,9),(4,7),(2,8),(5,6)
57: (1,9),(4,8),(2,7),(5,6)
58: (1,9),(6,5),(2,8),(7,4)
59: (1,9),(6,7),(3,4),(8,2)
60: (1,9),(6,8),(2,4),(7,3)
61: (2,1),(3,4),(6,5),(7,8)
62: (2,1),(4,6),(7,3),(9,8)
63: (2,1),(6,3),(4,5),(8,7)
64: (2,1),(6,3),(4,7),(8,9)
65: (2,1),(7,6),(3,4),(8,9)
66: (2,3),(1,4),(7,8),(6,9)
67: (2,3),(1,4),(9,5),(8,6)
68: (2,3),(1,8),(7,4),(6,9)
69: (2,3),(4,8),(5,1),(7,6)
70: (2,3),(5,7),(6,4),(9,8)
71: (2,3),(6,7),(1,4),(5,8)
72: (2,3),(6,7),(4,1),(8,5)
73: (2,3),(6,7),(5,4),(9,8)
74: (2,3),(6,8),(1,4),(5,9)
75: (2,3),(6,9),(4,1),(8,7)
76: (2,3),(8,5),(1,4),(7,6)
77: (2,4),(1,3),(8,6),(7,5)
78: (2,4),(1,6),(9,5),(8,7)
79: (2,4),(1,8),(7,5),(6,9)
80: (2,4),(3,8),(6,1),(7,5)
81: (2,4),(6,5),(3,8),(7,9)
82: (2,4),(6,8),(5,3),(9,7)
83: (2,4),(6,9),(1,3),(5,8)
84: (2,4),(7,9),(3,1),(8,6)
85: (2,4),(8,5),(3,6),(9,7)
86: (2,4),(8,6),(3,5),(9,7)
87: (2,5),(1,4),(7,9),(6,8)
88: (2,5),(1,7),(4,6),(3,8)
89: (2,5),(3,8),(6,1),(7,4)
90: (2,5),(3,9),(6,4),(7,8)
91: (2,5),(4,3),(7,8),(9,6)
92: (2,5),(4,6),(1,8),(3,9)
93: (2,5),(4,7),(1,6),(3,8)
94: (2,5),(6,1),(4,7),(8,3)
95: (2,5),(8,4),(3,7),(9,6)
96: (2,5),(8,6),(1,3),(7,4)
97: (2,5),(8,7),(3,4),(9,6)
98: (2,5),(9,4),(1,7),(8,6)
99: (2,5),(9,6),(1,3),(8,4)
100: (2,6),(1,5),(8,4),(7,3)
101: (2,6),(1,5),(9,4),(8,3)
102: (2,6),(1,7),(9,3),(8,4)
103: (2,6),(1,8),(4,5),(3,7)
104: (2,6),(1,9),(4,5),(3,8)
105: (2,6),(4,1),(5,8),(7,3)
106: (2,6),(4,1),(7,8),(9,3)
107: (2,6),(4,3),(7,8),(9,5)
108: (2,6),(4,8),(1,7),(3,9)
109: (2,6),(4,8),(5,1),(7,3)
110: (2,6),(8,4),(3,7),(9,5)
111: (2,6),(8,5),(1,4),(7,3)
112: (2,6),(8,7),(3,4),(9,5)
113: (2,6),(9,5),(1,4),(8,3)
114: (2,7),(1,6),(9,5),(8,4)
115: (2,7),(3,5),(8,6),(9,4)
116: (2,7),(3,6),(8,5),(9,4)
117: (2,7),(4,6),(3,9),(5,8)
118: (2,7),(4,9),(6,3),(8,5)
119: (2,7),(6,1),(4,9),(8,3)
120: (2,7),(6,3),(5,8),(9,4)
121: (2,7),(6,5),(4,3),(8,1)
122: (2,7),(6,8),(5,3),(9,4)
123: (2,7),(9,6),(1,4),(8,3)
124: (2,8),(1,6),(4,7),(3,5)
125: (2,8),(3,4),(6,5),(7,1)
126: (2,8),(3,5),(6,4),(7,1)
127: (2,8),(3,9),(4,6),(5,7)
128: (2,8),(3,9),(6,4),(7,5)
129: (2,8),(4,5),(7,6),(9,3)
130: (2,8),(4,9),(1,6),(3,7)
131: (2,8),(5,3),(4,6),(7,1)
132: (2,8),(5,6),(4,3),(7,1)
133: (2,8),(6,4),(1,7),(5,3)
134: (2,8),(6,7),(1,4),(5,3)
135: (2,8),(6,7),(5,4),(9,3)
136: (2,8),(6,9),(3,4),(7,5)
137: (2,8),(7,4),(1,9),(6,5)
138: (2,8),(7,6),(4,3),(9,1)
139: (2,8),(7,9),(1,3),(6,4)
140: (2,9),(1,7),(4,8),(3,6)
141: (2,9),(1,7),(5,8),(4,6)
142: (2,9),(1,8),(4,6),(3,5)
143: (2,9),(3,4),(7,6),(8,1)
144: (2,9),(4,7),(1,8),(3,6)
145: (2,9),(4,7),(6,3),(8,1)
146: (2,9),(4,8),(3,7),(5,6)
147: (2,9),(5,7),(1,8),(4,6)
148: (2,9),(6,4),(1,8),(5,3)
149: (2,9),(6,7),(4,3),(8,1)
150: (2,9),(7,4),(3,6),(8,1)
151: (2,9),(7,8),(1,4),(6,3)
152: (2,9),(7,8),(1,5),(6,4)
153: (3,1),(2,4),(7,5),(6,8)
154: (3,1),(4,5),(7,2),(8,6)
155: (3,1),(4,6),(8,2),(9,7)
156: (3,1),(4,8),(6,2),(7,9)
157: (3,1),(5,2),(4,7),(6,8)
158: (3,1),(5,8),(4,2),(6,9)
159: (3,1),(8,6),(2,4),(7,9)
160: (3,2),(1,4),(7,6),(5,8)
161: (3,2),(1,4),(8,7),(6,9)
162: (3,2),(1,5),(8,4),(6,7)
163: (3,2),(1,6),(7,4),(5,8)
164: (3,2),(1,6),(9,4),(7,8)
165: (3,2),(1,7),(8,4),(6,9)
166: (3,2),(4,1),(8,6),(9,5)
167: (3,2),(4,6),(7,5),(8,9)
168: (3,2),(4,7),(8,1),(9,6)
169: (3,2),(4,8),(5,1),(6,7)
170: (3,2),(5,4),(6,7),(8,9)
171: (3,2),(5,7),(6,4),(8,9)
172: (3,2),(6,9),(4,1),(7,8)
173: (3,2),(7,6),(4,5),(8,9)
174: (3,2),(8,5),(1,4),(6,7)
175: (3,4),(1,2),(9,8),(7,6)
176: (3,4),(1,8),(7,2),(5,6)
177: (3,4),(1,8),(9,2),(7,6)
178: (3,4),(2,8),(7,1),(6,5)
179: (3,4),(5,2),(7,8),(9,6)
180: (3,4),(7,2),(5,8),(9,6)
181: (3,4),(8,1),(2,9),(7,6)
182: (3,4),(8,2),(1,7),(6,5)
183: (3,4),(9,5),(2,6),(8,7)
184: (3,4),(9,6),(2,5),(8,7)
185: (3,5),(2,1),(7,8),(6,4)
186: (3,5),(4,1),(7,6),(8,2)
187: (3,5),(4,6),(1,7),(2,8)
188: (3,5),(4,6),(8,1),(9,2)
189: (3,5),(4,8),(1,6),(2,9)
190: (3,5),(8,2),(1,7),(6,4)
191: (3,5),(9,4),(2,7),(8,6)
192: (3,6),(1,2),(7,8),(5,4)
193: (3,6),(1,2),(9,8),(7,4)
194: (3,6),(1,5),(4,9),(2,8)
195: (3,6),(1,8),(9,2),(7,4)
196: (3,6),(1,9),(4,5),(2,8)
197: (3,6),(2,4),(9,7),(8,5)
198: (3,6),(2,9),(8,1),(7,4)
199: (3,6),(4,2),(8,5),(9,1)
200: (3,6),(4,8),(1,5),(2,7)
201: (3,6),(5,8),(2,7),(4,9)
202: (3,6),(7,5),(4,2),(8,1)
203: (3,6),(8,9),(2,1),(7,4)
204: (3,7),(1,5),(8,4),(6,2)
205: (3,7),(2,9),(5,6),(4,8)
206: (3,7),(4,8),(5,1),(6,2)
207: (3,7),(6,2),(5,9),(8,4)
208: (3,7),(8,9),(1,2),(6,4)
209: (3,8),(1,5),(4,9),(2,6)
210: (3,8),(4,1),(6,9),(7,2)
211: (3,8),(4,2),(5,7),(6,1)
212: (3,8),(4,6),(1,9),(2,7)
213: (3,8),(4,9),(5,1),(6,2)
214: (3,8),(5,2),(4,7),(6,1)
215: (3,8),(5,4),(7,6),(9,2)
216: (3,8),(5,9),(4,1),(6,2)
217: (3,8),(7,4),(1,6),(5,2)
218: (3,8),(7,6),(1,4),(5,2)
219: (3,8),(9,4),(1,6),(7,2)
220: (3,9),(1,6),(4,8),(2,5)
221: (3,9),(2,8),(5,7),(4,6)
222: (3,9),(4,6),(7,5),(8,2)
223: (3,9),(4,7),(1,8),(2,6)
224: (3,9),(5,7),(6,4),(8,2)
225: (3,9),(5,8),(4,2),(6,1)
226: (3,9),(7,6),(4,5),(8,2)
227: (3,9),(7,8),(2,5),(6,4)
228: (3,9),(8,4),(1,7),(6,2)
229: (3,9),(8,7),(1,4),(6,2)
230: (4,1),(3,2),(7,8),(6,9)
231: (4,1),(3,6),(9,2),(8,7)
232: (4,1),(5,8),(6,2),(7,9)
233: (4,1),(6,2),(3,7),(5,8)
234: (4,1),(8,2),(3,5),(7,6)
235: (4,1),(8,2),(5,6),(9,7)
236: (4,1),(8,7),(2,3),(6,9)
237: (4,1),(9,2),(3,5),(8,6)
238: (4,1),(9,3),(2,6),(7,8)
239: (4,1),(9,6),(2,3),(7,8)
240: (4,2),(1,3),(8,6),(5,7)
241: (4,2),(1,3),(9,7),(6,8)
242: (4,2),(3,1),(9,6),(8,5)
243: (4,2),(3,6),(9,1),(8,5)
244: (4,2),(3,9),(6,1),(5,8)
245: (4,2),(6,1),(3,8),(5,7)
246: (4,2),(6,1),(5,9),(7,8)
247: (4,2),(6,8),(5,3),(7,9)
248: (4,2),(7,9),(3,1),(6,8)
249: (4,2),(8,3),(1,6),(5,7)
250: (4,2),(8,3),(5,6),(9,7)
251: (4,2),(8,6),(3,5),(7,9)
252: (4,2),(8,7),(5,1),(9,6)
253: (4,2),(9,1),(3,7),(8,6)
254: (4,3),(2,1),(8,9),(6,7)
255: (4,3),(2,7),(8,1),(6,5)
256: (4,3),(2,7),(8,5),(6,9)
257: (4,3),(8,7),(1,2),(5,6)
258: (4,3),(9,6),(2,5),(7,8)
259: (4,5),(2,9),(8,3),(6,7)
260: (4,5),(3,2),(8,9),(7,6)
261: (4,5),(3,6),(2,8),(1,9)
262: (4,5),(3,7),(2,6),(1,8)
263: (4,5),(3,8),(2,6),(1,9)
264: (4,5),(9,6),(3,1),(8,2)
265: (4,6),(2,5),(3,9),(1,8)
266: (4,6),(3,2),(8,5),(7,1)
267: (4,6),(3,2),(8,9),(7,5)
268: (4,6),(3,2),(9,5),(8,1)
269: (4,6),(3,5),(2,9),(1,8)
270: (4,6),(3,5),(8,2),(7,1)
271: (4,6),(5,1),(8,7),(9,2)
272: (4,6),(5,2),(8,7),(9,3)
273: (4,6),(5,7),(8,1),(9,2)
274: (4,6),(5,8),(2,7),(3,9)
275: (4,6),(7,8),(2,1),(5,3)
276: (4,6),(8,2),(3,9),(7,5)
277: (4,6),(8,2),(5,7),(9,3)
278: (4,6),(9,2),(3,5),(8,1)
279: (4,6),(9,8),(2,1),(7,3)
280: (4,7),(1,2),(9,8),(6,3)
281: (4,7),(1,8),(9,2),(6,3)
282: (4,7),(1,9),(5,6),(2,8)
283: (4,7),(2,5),(3,8),(1,6)
284: (4,7),(2,6),(3,9),(1,8)
285: (4,7),(2,6),(5,9),(3,8)
286: (4,7),(3,5),(2,8),(1,6)
287: (4,7),(3,8),(6,1),(5,2)
288: (4,7),(5,3),(8,6),(9,2)
289: (4,7),(5,9),(1,6),(2,8)
290: (4,7),(8,2),(5,6),(9,1)
291: (4,7),(8,3),(2,5),(6,1)
292: (4,7),(8,6),(5,2),(9,1)
293: (4,7),(8,9),(2,1),(6,3)
294: (4,8),(1,7),(9,3),(6,2)
295: (4,8),(1,9),(5,6),(2,7)
296: (4,8),(2,5),(9,6),(7,3)
297: (4,8),(2,6),(3,9),(1,7)
298: (4,8),(3,6),(2,7),(1,5)
299: (4,8),(3,7),(6,2),(5,1)
300: (4,8),(3,9),(6,1),(5,2)
301: (4,8),(3,9),(7,1),(6,2)
302: (4,8),(5,9),(1,6),(2,7)
303: (4,8),(6,1),(5,9),(7,2)
304: (4,8),(6,9),(5,1),(7,2)
305: (4,8),(6,9),(5,2),(7,3)
306: (4,8),(7,9),(3,1),(6,2)
307: (4,8),(9,3),(2,6),(7,1)
308: (4,8),(9,7),(1,3),(6,2)
309: (4,9),(2,5),(8,7),(6,3)
310: (4,9),(2,6),(3,8),(1,5)
311: (4,9),(2,7),(8,3),(6,1)
312: (4,9),(3,5),(8,6),(7,2)
313: (4,9),(3,6),(8,5),(7,2)
314: (4,9),(3,7),(2,8),(1,6)
315: (4,9),(3,8),(6,2),(5,1)
316: (4,9),(3,8),(7,2),(6,1)
317: (4,9),(5,7),(1,8),(2,6)
318: (4,9),(5,7),(2,8),(3,6)
319: (4,9),(5,8),(1,7),(2,6)
320: (4,9),(6,2),(5,8),(7,1)
321: (4,9),(6,8),(3,2),(5,1)
322: (4,9),(8,7),(2,3),(6,1)
323: (5,1),(2,3),(7,6),(4,8)
324: (5,1),(2,6),(7,3),(4,8)
325: (5,1),(6,3),(8,2),(9,4)
326: (5,1),(6,7),(3,2),(4,8)
327: (5,1),(9,2),(4,6),(8,7)
328: (5,1),(9,6),(4,2),(8,7)
329: (5,2),(1,3),(8,6),(4,7)
330: (5,2),(3,1),(6,9),(4,8)
331: (5,2),(3,4),(8,7),(6,9)
332: (5,2),(3,7),(8,4),(6,9)
333: (5,2),(4,6),(9,3),(8,7)
334: (5,2),(6,1),(7,4),(8,3)
335: (5,2),(6,8),(3,1),(4,7)
336: (5,2),(8,1),(6,4),(9,3)
337: (5,2),(8,3),(1,6),(4,7)
338: (5,2),(9,1),(4,7),(8,6)
339: (5,3),(1,7),(8,2),(4,6)
340: (5,3),(4,9),(7,2),(6,8)
341: (5,3),(6,1),(8,4),(9,2)
342: (5,3),(6,4),(7,1),(8,2)
343: (5,3),(6,8),(1,4),(2,9)
344: (5,3),(7,1),(2,8),(4,6)
345: (5,3),(7,4),(6,1),(8,2)
346: (5,3),(8,7),(1,2),(4,6)
347: (5,4),(1,3),(6,8),(2,7)
348: (5,4),(1,3),(6,9),(2,8)
349: (5,4),(2,8),(9,3),(6,7)
350: (5,4),(3,2),(8,9),(6,7)
351: (5,4),(3,9),(8,2),(6,7)
352: (5,4),(6,3),(1,9),(2,8)
353: (5,4),(9,8),(2,3),(6,7)
354: (5,6),(7,1),(2,8),(4,3)
355: (5,6),(7,8),(2,1),(4,3)
356: (5,6),(8,2),(1,7),(4,3)
357: (5,7),(1,8),(6,3),(2,4)
358: (5,7),(2,6),(4,9),(1,8)
359: (5,7),(3,1),(6,8),(4,2)
360: (5,7),(4,2),(9,6),(8,1)
361: (5,7),(4,6),(9,2),(8,1)
362: (5,7),(4,9),(3,6),(2,8)
363: (5,7),(8,2),(3,9),(6,4)
364: (5,7),(9,3),(2,8),(6,4)
365: (5,7),(9,6),(4,3),(8,2)
366: (5,8),(1,7),(6,4),(2,3)
367: (5,8),(2,3),(7,6),(4,1)
368: (5,8),(3,1),(6,9),(4,2)
369: (5,8),(3,6),(4,9),(2,7)
370: (5,8),(4,9),(2,6),(1,7)
371: (5,8),(6,3),(1,9),(2,4)
372: (5,8),(6,7),(3,2),(4,1)
373: (5,8),(7,1),(4,9),(6,2)
374: (5,8),(7,3),(2,6),(4,1)
375: (5,8),(7,9),(4,1),(6,2)
376: (5,8),(9,6),(3,4),(7,2)
377: (5,9),(3,2),(6,8),(4,1)
378: (5,9),(4,2),(7,8),(6,1)
379: (5,9),(4,7),(2,8),(1,6)
380: (5,9),(4,7),(3,8),(2,6)
381: (5,9),(4,8),(7,2),(6,1)
382: (5,9),(6,2),(3,8),(4,1)
383: (5,9),(6,4),(1,8),(2,3)
384: (5,9),(7,3),(4,8),(6,2)
385: (6,1),(2,4),(7,5),(3,8)
386: (6,1),(2,5),(7,4),(3,8)
387: (6,1),(5,2),(4,8),(3,9)
388: (6,1),(5,2),(9,3),(8,4)
389: (6,1),(7,2),(8,4),(9,5)
390: (6,1),(7,8),(3,2),(4,9)
391: (6,1),(8,2),(5,3),(7,4)
392: (6,1),(8,2),(7,4),(9,5)
393: (6,1),(8,3),(5,2),(7,4)
394: (6,1),(8,5),(2,3),(4,7)
395: (6,2),(3,7),(8,4),(5,9)
396: (6,2),(4,1),(5,8),(3,7)
397: (6,2),(5,4),(8,1),(7,3)
398: (6,2),(5,4),(9,1),(8,3)
399: (6,2),(7,1),(8,5),(9,4)
400: (6,2),(7,8),(4,3),(5,9)
401: (6,2),(8,5),(1,4),(3,7)
402: (6,2),(8,7),(3,4),(5,9)
403: (6,3),(1,8),(7,4),(2,9)
404: (6,3),(4,2),(7,9),(5,8)
405: (6,3),(5,1),(8,4),(7,2)
406: (6,3),(5,4),(2,8),(1,9)
407: (6,3),(5,8),(2,4),(1,9)
408: (6,3),(7,1),(8,4),(9,2)
409: (6,3),(7,2),(4,9),(5,8)
410: (6,3),(7,4),(8,1),(9,2)
411: (6,3),(8,1),(2,9),(4,7)
412: (6,3),(8,2),(7,5),(9,4)
413: (6,3),(8,5),(2,7),(4,9)
414: (6,3),(8,5),(7,2),(9,4)
415: (6,3),(8,7),(2,1),(4,5)
416: (6,3),(9,1),(5,4),(8,2)
417: (6,3),(9,4),(2,7),(5,8)
418: (6,3),(9,4),(5,1),(8,2)
419: (6,3),(9,7),(2,4),(5,8)
420: (6,4),(1,8),(7,5),(2,9)
421: (6,4),(2,8),(7,5),(3,9)
422: (6,4),(2,9),(5,3),(1,8)
423: (6,4),(3,2),(8,9),(5,7)
424: (6,4),(5,2),(9,3),(8,1)
425: (6,4),(5,3),(2,8),(1,7)
426: (6,4),(5,3),(8,2),(7,1)
427: (6,4),(7,1),(2,8),(3,5)
428: (6,4),(7,5),(8,2),(9,3)
429: (6,4),(8,1),(7,5),(9,2)
430: (6,4),(8,3),(7,2),(9,1)
431: (6,4),(8,7),(1,2),(3,5)
432: (6,4),(9,8),(2,3),(5,7)
433: (6,5),(1,2),(8,7),(3,4)
434: (6,5),(1,4),(7,9),(2,8)
435: (6,5),(2,1),(7,8),(3,4)
436: (6,5),(7,9),(2,4),(3,8)
437: (6,5),(8,4),(7,3),(9,2)
438: (6,5),(8,9),(2,3),(4,7)
439: (6,7),(1,9),(8,2),(3,4)
440: (6,7),(2,5),(8,3),(4,1)
441: (6,7),(2,8),(5,3),(1,4)
442: (6,7),(5,8),(4,1),(3,2)
443: (6,7),(8,1),(2,9),(4,3)
444: (6,7),(8,5),(2,3),(4,1)
445: (6,7),(9,2),(1,8),(4,3)
446: (6,7),(9,8),(1,2),(4,3)
447: (6,8),(2,4),(9,7),(5,3)
448: (6,8),(2,7),(5,4),(1,3)
449: (6,8),(2,7),(9,4),(5,3)
450: (6,8),(4,1),(7,9),(5,2)
451: (6,8),(4,2),(7,9),(5,3)
452: (6,8),(4,9),(5,1),(3,2)
453: (6,8),(5,7),(4,2),(3,1)
454: (6,8),(5,9),(4,1),(3,2)
455: (6,8),(7,1),(3,9),(4,2)
456: (6,8),(7,1),(4,9),(5,2)
457: (6,8),(7,3),(1,9),(2,4)
458: (6,8),(7,4),(1,9),(2,5)
459: (6,8),(7,4),(2,5),(3,1)
460: (6,8),(7,4),(2,9),(3,5)
461: (6,8),(9,3),(1,7),(4,2)
462: (6,9),(1,5),(7,8),(2,4)
463: (6,9),(2,4),(5,8),(1,3)
464: (6,9),(2,5),(7,8),(3,4)
465: (6,9),(4,3),(7,8),(5,2)
466: (6,9),(4,8),(7,2),(5,1)
467: (6,9),(4,8),(7,3),(5,2)
468: (6,9),(5,2),(4,8),(3,1)
469: (6,9),(7,2),(3,8),(4,1)
470: (6,9),(7,5),(2,8),(3,4)
471: (6,9),(7,8),(4,2),(5,1)
472: (6,9),(8,3),(2,7),(4,1)
473: (6,9),(8,7),(2,5),(4,3)
474: (7,1),(2,6),(8,4),(3,9)
475: (7,1),(4,2),(6,8),(3,9)
476: (7,1),(4,8),(6,2),(3,9)
477: (7,1),(6,2),(9,3),(8,4)
478: (7,1),(6,8),(5,2),(4,9)
479: (7,1),(8,3),(5,2),(6,4)
480: (7,1),(8,6),(2,4),(3,9)
481: (7,1),(9,6),(2,3),(4,8)
482: (7,2),(1,4),(9,6),(3,8)
483: (7,2),(3,6),(9,4),(5,8)
484: (7,2),(5,3),(6,8),(4,9)
485: (7,2),(5,6),(3,4),(1,8)
486: (7,2),(6,1),(4,9),(3,8)
487: (7,2),(6,3),(5,8),(4,9)
488: (7,2),(6,4),(9,1),(8,3)
489: (7,2),(6,4),(9,3),(8,5)
490: (7,2),(8,6),(3,1),(4,5)
491: (7,3),(5,9),(6,2),(4,8)
492: (7,3),(6,1),(9,4),(8,2)
493: (7,3),(9,2),(6,5),(8,4)
494: (7,3),(9,5),(2,6),(4,8)
495: (7,4),(5,2),(3,8),(1,6)
496: (7,4),(5,8),(3,2),(1,6)
497: (7,4),(6,1),(9,5),(8,2)
498: (7,4),(6,3),(2,9),(1,8)
499: (7,4),(6,8),(3,1),(2,5)
500: (7,4),(6,8),(3,5),(2,9)
501: (7,4),(6,9),(2,3),(1,8)
502: (7,4),(8,3),(1,6),(2,5)
503: (7,4),(9,3),(6,2),(8,1)
504: (7,4),(9,5),(6,2),(8,3)
505: (7,4),(9,8),(3,2),(5,6)
506: (7,5),(2,3),(9,8),(4,6)
507: (7,5),(2,8),(9,3),(4,6)
508: (7,5),(2,9),(6,4),(1,8)
509: (7,5),(3,1),(6,8),(2,4)
510: (7,5),(3,6),(8,1),(4,2)
511: (7,5),(8,3),(1,6),(2,4)
512: (7,5),(9,2),(6,4),(8,1)
513: (7,6),(2,1),(8,9),(3,4)
514: (7,6),(2,3),(9,8),(4,5)
515: (7,6),(2,8),(9,3),(4,5)
516: (7,6),(3,8),(5,2),(1,4)
517: (7,6),(3,8),(9,2),(5,4)
518: (7,6),(3,9),(8,2),(4,5)
519: (7,6),(5,8),(4,1),(2,3)
520: (7,6),(8,4),(1,5),(2,3)
521: (7,6),(8,5),(3,2),(4,1)
522: (7,6),(9,1),(2,8),(4,3)
523: (7,8),(1,4),(9,6),(3,2)
524: (7,8),(2,9),(6,3),(1,4)
525: (7,8),(3,4),(6,9),(2,5)
526: (7,8),(3,5),(6,4),(2,1)
527: (7,8),(5,3),(4,6),(2,1)
528: (7,8),(5,4),(3,6),(1,2)
529: (7,8),(5,6),(4,3),(2,1)
530: (7,8),(6,1),(4,9),(3,2)
531: (7,8),(6,2),(5,9),(4,3)
532: (7,8),(6,9),(2,4),(1,5)
533: (7,8),(6,9),(5,1),(4,2)
534: (7,8),(6,9),(5,2),(4,3)
535: (7,8),(9,4),(3,6),(5,2)
536: (7,8),(9,5),(2,6),(4,3)
537: (7,8),(9,6),(3,4),(5,2)
538: (7,9),(2,5),(6,8),(1,4)
539: (7,9),(2,6),(8,4),(3,1)
540: (7,9),(6,3),(5,8),(4,2)
541: (7,9),(6,4),(2,8),(1,3)
542: (7,9),(6,8),(4,2),(3,1)
543: (7,9),(6,8),(5,2),(4,1)
544: (7,9),(8,5),(3,6),(4,2)
545: (8,1),(3,2),(9,6),(4,7)
546: (8,1),(3,6),(9,2),(4,7)
547: (8,1),(5,3),(9,2),(6,4)
548: (8,1),(6,2),(7,3),(5,4)
549: (8,1),(6,2),(9,4),(7,5)
550: (8,1),(9,2),(6,3),(7,4)
551: (8,2),(3,6),(9,1),(4,5)
552: (8,2),(4,6),(5,3),(1,7)
553: (8,2),(4,6),(7,1),(3,5)
554: (8,2),(4,6),(9,3),(5,7)
555: (8,2),(4,7),(9,1),(5,6)
556: (8,2),(5,4),(6,7),(3,9)
557: (8,2),(6,3),(9,4),(7,5)
558: (8,2),(6,5),(3,4),(1,7)
559: (8,2),(6,5),(9,1),(7,4)
560: (8,2),(9,3),(6,4),(7,5)
561: (8,2),(9,7),(3,1),(4,6)
562: (8,2),(9,7),(4,1),(5,6)
563: (8,3),(1,6),(9,4),(2,7)
564: (8,3),(4,1),(6,7),(2,5)
565: (8,3),(4,1),(6,9),(2,7)
566: (8,3),(4,2),(9,7),(5,6)
567: (8,3),(4,7),(5,2),(1,6)
568: (8,3),(5,1),(9,4),(6,2)
569: (8,3),(5,7),(4,2),(1,6)
570: (8,3),(6,4),(7,1),(5,2)
571: (8,3),(6,7),(4,5),(2,9)
572: (8,4),(1,3),(9,7),(2,6)
573: (8,4),(1,6),(9,3),(2,5)
574: (8,4),(2,5),(9,6),(3,7)
575: (8,4),(2,6),(9,5),(3,7)
576: (8,4),(3,2),(6,9),(1,7)
577: (8,4),(3,7),(6,2),(1,5)
578: (8,4),(5,2),(6,9),(3,7)
579: (8,4),(5,3),(9,2),(6,1)
580: (8,4),(6,2),(3,9),(1,7)
581: (8,4),(6,3),(7,2),(5,1)
582: (8,4),(6,3),(9,2),(7,1)
583: (8,4),(6,5),(9,1),(7,2)
584: (8,4),(7,1),(3,9),(2,6)
585: (8,4),(7,9),(3,1),(2,6)
586: (8,4),(9,5),(6,1),(7,2)
587: (8,4),(9,6),(1,5),(2,7)
588: (8,5),(1,3),(9,6),(2,4)
589: (8,5),(1,4),(9,7),(2,6)
590: (8,5),(1,7),(9,4),(2,6)
591: (8,5),(2,7),(9,4),(3,6)
592: (8,5),(3,2),(6,7),(1,4)
593: (8,5),(4,1),(7,6),(3,2)
594: (8,5),(4,2),(7,9),(3,6)
595: (8,5),(4,7),(6,1),(2,3)
596: (8,5),(6,9),(4,3),(2,7)
597: (8,5),(7,1),(4,6),(3,2)
598: (8,5),(7,2),(4,9),(3,6)
599: (8,5),(7,3),(2,6),(1,4)
600: (8,5),(7,6),(2,3),(1,4)
601: (8,5),(9,2),(6,4),(7,1)
602: (8,5),(9,3),(1,6),(2,4)
603: (8,5),(9,4),(6,2),(7,1)
604: (8,5),(9,4),(6,3),(7,2)
605: (8,6),(1,5),(9,4),(2,3)
606: (8,6),(2,4),(7,5),(1,3)
607: (8,6),(4,7),(9,2),(5,3)
608: (8,6),(4,9),(7,2),(3,5)
609: (8,6),(7,1),(3,9),(2,4)
610: (8,6),(7,9),(4,2),(3,5)
611: (8,6),(9,3),(1,7),(2,4)
612: (8,6),(9,5),(3,2),(4,1)
613: (8,6),(9,7),(1,3),(2,4)
614: (8,6),(9,7),(1,4),(2,5)
615: (8,6),(9,7),(2,4),(3,5)
616: (8,6),(9,7),(4,1),(5,2)
617: (8,7),(1,5),(9,6),(2,4)
618: (8,7),(3,2),(6,9),(1,4)
619: (8,7),(3,2),(9,6),(4,1)
620: (8,7),(3,4),(6,5),(1,2)
621: (8,7),(3,9),(6,2),(1,4)
622: (8,7),(4,3),(6,9),(2,5)
623: (8,7),(4,9),(6,1),(2,3)
624: (8,7),(4,9),(6,3),(2,5)
625: (8,7),(5,2),(6,9),(3,4)
626: (8,7),(5,3),(4,6),(1,2)
627: (8,7),(5,6),(4,3),(1,2)
628: (8,7),(5,9),(6,2),(3,4)
629: (8,7),(9,4),(1,6),(2,3)
630: (8,7),(9,6),(1,4),(2,3)
631: (8,7),(9,6),(4,3),(5,2)
632: (8,9),(4,7),(6,5),(2,3)
633: (8,9),(6,4),(3,7),(1,2)
634: (8,9),(6,7),(4,3),(2,1)
635: (8,9),(7,4),(3,6),(2,1)
636: (9,1),(4,2),(8,6),(3,7)
637: (9,1),(6,3),(8,2),(5,4)
638: (9,1),(7,2),(8,4),(6,5)
639: (9,1),(7,4),(8,2),(6,5)
640: (9,1),(8,2),(4,5),(3,6)
641: (9,1),(8,3),(6,2),(5,4)
642: (9,2),(4,1),(8,6),(3,5)
643: (9,2),(6,3),(4,7),(1,8)
644: (9,2),(6,7),(4,3),(1,8)
645: (9,2),(7,1),(8,5),(6,4)
646: (9,2),(8,1),(4,7),(3,6)
647: (9,2),(8,1),(6,4),(5,3)
648: (9,2),(8,7),(4,1),(3,6)
649: (9,3),(4,2),(6,8),(1,7)
650: (9,3),(4,6),(7,5),(2,8)
651: (9,3),(4,8),(7,1),(2,6)
652: (9,3),(6,1),(8,4),(5,2)
653: (9,3),(6,4),(5,7),(2,8)
654: (9,3),(7,4),(8,1),(6,2)
655: (9,3),(8,4),(2,6),(1,7)
656: (9,3),(8,4),(7,1),(6,2)
657: (9,3),(8,5),(7,2),(6,4)
658: (9,3),(8,6),(2,4),(1,7)
659: (9,4),(2,3),(8,7),(1,6)
660: (9,4),(2,6),(8,3),(1,5)
661: (9,4),(5,2),(7,8),(3,6)
662: (9,4),(5,8),(7,2),(3,6)
663: (9,4),(6,2),(8,3),(5,1)
664: (9,4),(7,2),(3,8),(1,6)
665: (9,4),(8,1),(7,5),(6,2)
666: (9,4),(8,2),(7,3),(6,1)
667: (9,4),(8,5),(2,6),(1,7)
668: (9,4),(8,6),(2,5),(1,7)
669: (9,5),(2,7),(8,4),(1,6)
670: (9,5),(7,3),(4,8),(2,6)
671: (9,5),(7,4),(8,3),(6,2)
672: (9,5),(8,1),(4,6),(3,2)
673: (9,6),(3,2),(7,8),(1,4)
674: (9,6),(4,1),(7,8),(2,3)
675: (9,6),(4,2),(8,5),(3,1)
676: (9,6),(4,8),(7,1),(2,3)
677: (9,6),(4,8),(7,3),(2,5)
678: (9,6),(5,2),(8,7),(4,3)
679: (9,6),(7,2),(3,8),(1,4)
680: (9,6),(8,1),(5,7),(4,2)
681: (9,6),(8,2),(4,5),(3,1)
682: (9,6),(8,2),(5,7),(4,3)
683: (9,6),(8,3),(2,7),(1,4)
684: (9,6),(8,4),(2,7),(1,5)
685: (9,6),(8,7),(2,3),(1,4)
686: (9,6),(8,7),(4,1),(3,2)
687: (9,7),(4,2),(6,8),(1,3)
688: (9,7),(5,2),(8,6),(4,1)
689: (9,7),(6,2),(4,8),(1,3)
690: (9,7),(6,3),(5,8),(2,4)
691: (9,7),(8,4),(2,6),(1,3)
692: (9,7),(8,6),(2,5),(1,4)
693: (9,8),(3,4),(7,6),(1,2)
694: (9,8),(4,5),(7,6),(2,3)
695: (9,8),(5,6),(7,4),(3,2)
696: (9,8),(7,5),(4,6),(2,3)

Source: Daniel Torres-Rangel

## Similar Triangles 2

Directions: Using the digits 0 to 9 at most one time each, create two similar …

1. I only found eight possible solutions, but I’m willing to be wrong.
All are transformations of the first solution given – reflect it over the midline (y = 4.5) for another, over the other midline (x = 4.5) and across the line y = x. This gives you four solutions that all have rotational symmetry with each other about a circle centered at (4.5, 4.5).
To get the other four solutions translate the first four solutions by the vector .

2. (1,7)
(6,5)
(3,4)
(8,2)

3. How were all 696 solutions found? Brute force, algorithm, or some other way? I’m also curious if there is a way to prove that there are 696 unique solutions without actually finding them.

4. I found #39 very helpful because it made a rectangle, and I found at another source that said a rectangle is a special kind of parallelogram. I would like to say that I believe that not all those answers are correct on a coordinate plane but I found one so I am happy!

5. The areas of these parallelograms are all in the range [1,29]
Ex: #33: (1,6),(2,7),(4,8),(5,9) –> area=1
#106: (2,6),(4,1),(7,8),(9,3) –> area=29

• Between these parallelograms there are five different squares.
* area=5 Ex #40: (1,7),(2,9),(3,6),(4,8)
* area=17 Ex #44: (1,7),(5,8),(2,3),(6,4)
* area=20 Ex #163: (3,2),(1,6),(7,4),(5,8)
* area=26 Ex #68: (2,3),(1,8),(7,4),(6,9)
* area=29 Ex #106: (2,6),(4,1),(7,8),(9,3)

Beyond these squares there are five other different rectangles.
* area=4 Ex #39: (1,7),(2,8),(3,5),(4,6)
* area=8 Ex #17: (1,4),(5,8),(2,3),(6,7)
* area=10 Ex #21: (1,4),(6,9),(2,3),(7,8)
* area=16 Ex #18: (1,4),(5,8),(3,2),(7,6)
* area=20 Ex #75: (2,3),(6,9),(4,1),(8,7)

And beyond the five squares there are another five different rhombuses.
* area=3 Ex #298: (4,8),(3,6),(2,7),(1,5)
* area=12 Ex #63: (2,1),(6,3),(4,5),(8,7)
* area=15 Ex #47: (1,8),(2,4),(5,7),(6,3)
* area=21 Ex #59: (1,9),(6,7),(3,4),(8,2)
* area=24 Ex #60: (1,9),(6,8),(2,4),(7,3)