What numbers is a multiple of 3 greater than 25 less than 49 whose product of its two digits is a perfect cube what are the three answers?

Answer 1

I can only find two solutions.

The number must be a 2-digit number (as it is between 25 and 49).Let the number be represented by the digits a and b

Then a x b = n3

When n = 1, n3 = 1 and thus a = b = 1. ab is therefore 11 and outside the permitted range.

When n = 2, n3 = 8 and the two pairs of possible digits are 1 & 8, and 4 & 2.

18, 81 and 24 are outside the permitted range leaving only 42.

When n = 3, n3 = 27 and the pairs of possible digits are 3 & 9. The only combination within the permitted range is 39.

When n = 4, n3 = 64. The only possible combination is 88 which is not a multiple of 3 and is also outside the permitted range

For n = 5 and greater, n3 is a 3 digit number and cannot therefore be obtained as a product of two single digit numbers.

The two answers are therefore 39 (3 x 9 = 27 = 33) and 42 (4 x 2 = 8 = 23)

Answer 2

13