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Question

Arrange the numbers $1$ to $9$ to replace letters $A$ to $I$ so:
$(A+B+C+D)-(E+F+G+H) = I$
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Then explain why.

MrSethward · Accepted Answer

#1

#2

Thus:

Corleone · Answer

Kable · Answer

Thought I'd share my algebraic solution
We know:

And:

Therefore:

tarun jain · Answer

Adding or subtracting 2 odd/even numbers is even.
From 1 - 9 we have 5 odd numbers and 4 even numbers.
The above equation

Can be rearranged as

Adding or subtracting 4 even numbers will result in even number similarly adding or subtracting 4 odd numbers will be even. So we are left with 1 odd number

Results in

Which is not possible since even plus odd is always odd.

karu · Answer

A slightly shorter answer:

athin · Answer

The equation is equivalent to:

As $A$ to $I$ are $1$ to $9$:

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