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The number 132 is a three digit number with three distinct digits that is equal to the sum of all two digit numbers that are made up of its three digits:
![\[132=12+13+21+23+31+32\]](https://conundrum.wycombeabbey.com/wp-content/ql-cache/quicklatex.com-d844acaf65f9bf2f9d3e7c47f778d67b_l3.svg "Rendered by QuickLaTeX.com")
What is the largest three digit number with this property?
Incorrect
In the sum on the right, each digit appears twice in the tens column and twice in the units column. So if the digits are 
and 
we have
If 
this equation becomes 
, but this has no solutions as the right-hand-side is at most 
(as 
and are both at most 
. If 
then the equation becomes 
. For values of between 
and , 
is a multiple of 
only when 
or 
, and only gives a value of that is between and (
). So the largest values is 
.
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