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:

Set 1: 11×11=4
Set 2: 22×22=16
Set 3: 33×33=?

For first set
Method 1   11×11=121 then summing the digits in the products give us 1+2+1=4
Method 2   (1+1) x (1+1) = 4

and for second set
Method 1  22×22=484 then summing the digits in the product gives us 4+8+4=16
Method 2  (2+2) x (2+2) = 16

But when it comes to the next set of 33×33=? each solution diverges and will yield two different results (see result bellow for method 1 and 2).

Method 1 (sum of the digits in the product) it is: 33×33=18

33×33=1089 or 1+0+8+9= 18

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

Here are the solution for the first 40 sets for each method.

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

image

imageimage

It is interesting to note the series growth patterns for each method.  Where in method 1, the values tend to cluster around a range of several values (see pattern for 30K solutions), in method 2 the growth is polynomial.

 

© Copyright 2017 Yaacov Apelbaum, All Rights Reserved.

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