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, 25, ...81. The only one of these six that works (multiplies to three digits, not more) 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 January 13, 2022, 10:44 am
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