Maths Super Challenge 33
14 May 2020
We need to make the hundreds digit as small as possible to make the smallest sum. They have to be different non-zero digits so let's try 1,2 and 3.
Now look at the tens digit. Well that can be 0 so A can be zero.
Now look at the ones digit. Choose the smallest digits not yet used - 4 and 5.
T, B, M are 1,2,3 and it doesn't matter which is which.
A = 0
P, N are 4,5 and it doesn't matter which is which.
So we have
TAP + BAT + MAN
104 + 201 + 305 = 610
The smallest sum is 610.