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Only a Math Genius can Solve this Puzzle–Not Really!

 

Yaacov Apelbaum Sumerian mathematic tablet

 

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

Yaacov Apelbaum If X and Y than Z

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

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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

Yaacov Apelbaum - How many four sided figures

 

© Copyright 2017 Yaacov Apelbaum, All Rights Reserved.

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