Today Puzzle #685
Puzzle No. 685鈥� Thursday 27 February
Find a two-digit number which is 6 times as large as the sum of its digits.
Today’s #PuzzleForToday has been set by Dr Nicos Georgiou, a senior mathematics lecturer from the University of Sussex.
Click here for the answer
Denote the digits by x and y. Then the number is 10x + y and the sum of the digits is x + y. Then the equation we have is
6(x + y) = 10 x + y
That after re-arrangement the equation becomes 5y = 4x. Now, x can be 1, 2, …, 9, and y = 0, 1, 2, …, 9. The only possible solutions is y = 4 and x = 5, and the number is 54.
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