Teaser 2509

[Cactus]

Sunday Times Teaser 2509 by Andrew Skidmore
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I have three different numbers, each in the range 1 to 49 inclusive.
I then created two six digit numbers by joining them together in both
ascending and descending order. I took the difference between these
two numbers, multiplied it by three and divided the result by the sum
of my three original numbers. I then divided this result by one of my
original numbers and obtained another of them. In ascending order,
what were my original three numbers.

Cactus

[Peter]

Good morning all,

the difference of the 6-digit numbers, composed of x<y<z, can be
written as d = 9*11*101*(z - x).
With s = x+y+z one has three options, 3*d/s = x*y or x*z or y*z. An
integer solution requires s = 101. I found the answer for the option
27*11*(z-x)= y*z.

Peter

[Garry]

Hello Peter

My solution has 3*d/s = 1188, which will be the same as yours..

Presumably, each number was to be in the range 11 to 49 inclusive, as
they had to have two digits.

Garry