# Sunday Times Teaser 3132 – Bilateral Symmetry

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

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