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Saturday, 24 August 2019

"A Puzzle A Day" - add nine, reverse digits

This puzzle is one of those which is almost as simple to solve as it is to state:

Find a two-digit number that reverses its digits when you add nine to it.

Knowing that the nine-times table contains numbers which have two series of ascending tens and descending units, this should be a case of just identifying a pair:

9, 18, 27, 36, 45, 54, 63, etc.

However, there are many more pairs of numbers that fit the requirement in the question:

23 and 32
34 and 43
45 and 54 we've already mentioned
56 and 65
and so on

Any two digit number of the form (10x + (x+1)) or 11x+1 will reverse its digits when adding nine (up to 89 + 9 = 98).

The situation changes above 100, and its not possible to reverse digits by adding just nine (and we have three-digit numbers).


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