Let's calculate the products and check if they indeed have the same value:
Product of 32 and 46:
32 * 46 = 1,472
Reverse the digits of 23 and 64:
23 * 64 = 1,472
As you mentioned, the products are the same. This phenomenon is not unique to this particular pair of numbers. In fact, it occurs with any pair of two-digit numbers whose digits, when reversed, are the same as the product of the original numbers.
To find two other pairs of two-digit numbers that have this property, we can explore a few examples:
Product of 13 and 62:
13 * 62 = 806
Reversed digits: 31 * 26 = 806
Product of 17 and 83:
17 * 83 = 1,411
Reversed digits: 71 * 38 = 1,411
As for determining if a given pair of two-digit numbers will have this property without actually performing the multiplication, there is a simple rule. For any pair of two-digit numbers (AB and CD), if the sum of A and D equals the sum of B and C, then the products of the original and reversed digits will be the same.
For example, let's consider the pair 25 and 79:
A = 2, B = 5, C = 7, D = 9
The sum of A and D is 2 + 9 = 11, and the sum of B and C is 5 + 7 = 12. Since the sums are not equal (11 ≠ 12), we can determine that the products of the original and reversed digits will not be the same for this pair.
Therefore, by checking the sums of the digits in the two-digit numbers, we can determine whether they will have the property of the products being the same when digits are reversed.