Only a Math Genius can Solve this Puzzle–Not Really!
One of the most popular math equation puzzles on social media is interesting because it doesn’t have one correct answer and it illustrates the nature of a solution divergence.
Here is an example. The following two problems can be solved correctly regardless if we use sum of the digits in the product or product of the sum of digits methods:
11×11=4
22×22=16
But when it comes to the next set of 33×33=? each solution diverges and will yield two different results (see result table bellow for method 1 and 2).
For method 1 (sum of the digits in the product) it is: 33×33=18
33×33=1089 or 1+0+8+9= 18
For method 2 (product of the sum of digits) it is: 33×33=36
(3+3)x(3+3) = (6)x(6)=36
Here is a graphic solution for method 2
Method 1 | Method 2 | ||||||
11 | 11 | 121 | 4 | 11 | 11 | 4 | |
22 | 22 | 484 | 16 | 22 | 22 | 16 | |
33 | 33 | 1089 | 18 | 33 | 33 | 36 | |
44 | 44 | 1936 | 19 | 44 | 44 | 64 | |
55 | 55 | 3025 | 10 | 55 | 55 | 100 | |
66 | 66 | 4356 | 18 | 66 | 66 | 144 | |
77 | 77 | 5929 | 25 | 77 | 77 | 196 | |
88 | 88 | 7744 | 22 | 88 | 88 | 256 | |
99 | 99 | 9801 | 18 | 99 | 99 | 324 | |
110 | 110 | 12100 | 4 | 110 | 110 | 400 | |
121 | 121 | 14641 | 16 | 121 | 121 | 484 | |
132 | 132 | 17424 | 18 | 132 | 132 | 576 | |
143 | 143 | 20449 | 19 | 143 | 143 | 676 | |
154 | 154 | 23716 | 19 | 154 | 154 | 784 | |
165 | 165 | 27225 | 18 | 165 | 165 | 900 | |
176 | 176 | 30976 | 25 | 176 | 176 | 1024 | |
187 | 187 | 34969 | 31 | 187 | 187 | 1156 | |
198 | 198 | 39204 | 18 | 198 | 198 | 1296 | |
209 | 209 | 43681 | 22 | 209 | 209 | 1444 | |
220 | 220 | 48400 | 16 | 220 | 220 | 1600 | |
231 | 231 | 53361 | 18 | 231 | 231 | 1764 | |
242 | 242 | 58564 | 28 | 242 | 242 | 1936 | |
253 | 253 | 64009 | 19 | 253 | 253 | 2116 | |
264 | 264 | 69696 | 36 | 264 | 264 | 2304 | |
275 | 275 | 75625 | 25 | 275 | 275 | 2500 | |
286 | 286 | 81796 | 31 | 286 | 286 | 2704 | |
297 | 297 | 88209 | 27 | 297 | 297 | 2916 | |
308 | 308 | 94864 | 31 | 308 | 308 | 3136 | |
319 | 319 | 101761 | 16 | 319 | 319 | 3364 | |
330 | 330 | 108900 | 18 | 330 | 330 | 3600 | |
341 | 341 | 116281 | 19 | 341 | 341 | 3844 | |
352 | 352 | 123904 | 19 | 352 | 352 | 4096 | |
363 | 363 | 131769 | 27 | 363 | 363 | 4356 | |
374 | 374 | 139876 | 34 | 374 | 374 | 4624 | |
385 | 385 | 148225 | 22 | 385 | 385 | 4900 | |
396 | 396 | 156816 | 27 | 396 | 396 | 5184 | |
407 | 407 | 165649 | 31 | 407 | 407 | 5476 | |
418 | 418 | 174724 | 25 | 418 | 418 | 5776 | |
429 | 429 | 184041 | 18 | 429 | 429 | 6084 | |
440 | 440 | 193600 | 19 | 440 | 440 | 6400 |
It is interesting to also note the series growth patterns for each method. Where in method 1, the values tend to cluster around, in method 2 the growth is polynomial.
© Copyright 2017 Yaacov Apelbaum, All Rights Reserved.
How many four-sided figures appear in the diagram?
There are a number of these geometric combinometrics problems around. Here is a complete graphic solution to the one of the more common ones.
Question: How many four-sided figures appear in the diagram below?
- 10
- 16
- 22
- 25
- 28
Answer: 25
© Copyright 2017 Yaacov Apelbaum, All Rights Reserved.