a.What is the only three-digit number that is equal to a square number multiplied by the reverse of the same square number?

b.What is the largest three-digit number that is equal to a number multiplied by the reverse of the same number?

No zeroes in your reversals.

a. Since, only 2 two-digit numbers when multiplied give three digit numbers (as opposed to 2 one- or 2 three-digit numbers) we look to the two digit squares: 16, 36, ...81. The only one that works is 16 * 61 = 976

b. Again we are multiplying 2 two-digit numbers, say ab and its reverse: ba.

ab x ba = (a+10b)(10a+b) <999

a^2+2ab+b^2 = (a+b)^2 < 99

a+b <= 9

only 20 (unreversed) numbers satisfies this:

18 17 27 16 26 36 15 25 35 45 14 24 34 44 13 23 33 12 22 11,

and, of these, 16 wins the prize again as 16 * 61 = 976.

*Edited on ***November 4, 2018, 10:29 pm**