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Sunday Times Teaser 3132 – Bilateral Symmetry

by Brian Gladman on September 30, 2022

by Susan Bricket

Published Sunday October 02 2022 (link)

My son, at a loose end after A-levels, asked me for a mental challenge. As we’d been discussing palindromes, I suggested he try to find an arrangement of the digits 1 to 9 with the multiplication symbol “x” to give a palindrome as the answer, and he came up with 29678 x 1453 = 43122134. I said: “Now try to find the smallest such palindromic product starting in 4, where the last digit of the smallest number is still 3”. He found that smallest product, and, interestingly, if he added the two smaller numbers instead of multiplying them, then added 100, he also got a palindrome.

What was the smallest product?

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3 Comments Leave one →
  1. Brian Gladman permalink

    Updated to use Frits’ simple optimisation (see below).

  2. Frits permalink

    • Brian Gladman permalink

      A nice simple optimisation for the ‘8’ that I should have noticed!

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