SOLUTION: Find the product of 32 and 46. Now reverse the digits and find the product of 23 and 64. The products are the same. Does this happen with any pair of two-digit numbers? Find two ot

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Question 265287: Find the product of 32 and 46. Now reverse the digits and find the product of 23 and 64. The products are the same. Does this happen with any pair of two-digit numbers? Find two other pairs of two-digit numbers (with different digits) that have this property. Note: You cannot use the same answers another student has already posted. Explain your thinking in solving this problem and also include any mathematical work.
Answer by Edwin McCravy(20054)   (Show Source): You can put this solution on YOUR website!

Suppose the two digit numbers are "10A+B" and "10C+D:, then

(10A+B)(10C+D) = (10B+A)(10D+C)

That simplifies to

AC = BD

so the reason 32 x 46 = 23 x 64 is because the product of the tens digits
of 32 and 46 (3x4 equals the product of the units digits 2x6).

All the possibilities are below:

1.  21 × 24 = 504 and 12 × 42 = 504
2.  21 × 36 = 756 and 12 × 63 = 756
3.  21 × 48 = 1008 and 12 × 84 = 1008
4.  31 × 26 = 806 and 13 × 62 = 806
5.  31 × 39 = 1209 and 13 × 93 = 1209
6.  32 × 46 = 1472 and 23 × 64 = 1472
7.  32 × 69 = 2208 and 23 × 96 = 2208
8.  41 × 28 = 1148 and 14 × 82 = 1148
9.  42 × 12 = 504 and 24 × 21 = 504
10.  42 × 36 = 1512 and 24 × 63 = 1512
11.  42 × 48 = 2016 and 24 × 84 = 2016
12.  43 × 68 = 2924 and 34 × 86 = 2924
13.  62 × 13 = 806 and 26 × 31 = 806
14.  62 × 39 = 2418 and 26 × 93 = 2418
15.  63 × 12 = 756 and 36 × 21 = 756
16.  63 × 24 = 1512 and 36 × 42 = 1512
17.  63 × 48 = 3024 and 36 × 84 = 3024
18.  64 × 23 = 1472 and 46 × 32 = 1472
19.  64 × 69 = 4416 and 46 × 96 = 4416
20.  82 × 14 = 1148 and 28 × 41 = 1148
21.  84 × 12 = 1008 and 48 × 21 = 1008
22.  84 × 24 = 2016 and 48 × 42 = 2016
23.  84 × 36 = 3024 and 48 × 63 = 3024
24.  86 × 34 = 2924 and 68 × 43 = 2924
25.  93 × 13 = 1209 and 39 × 31 = 1209
26.  93 × 26 = 2418 and 39 × 62 = 2418
27.  96 × 23 = 2208 and 69 × 32 = 2208
28.  96 × 46 = 4416 and 69 × 64 = 4416

Edwin
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