ABC addition
Can you work out what a, b and c are in this sum?
Age
11 to 14
Challenge level
Problem
In this addition, $a$, $b$ and $c$ each represent a single digit.
Image
What number does $abc$ represent?
This problem is taken from the UKMT Mathematical Challenges.
Student Solutions
Answer: $367$
Image
Either $a=4$ and $c+b = 4$,
Or $a=3$ and $c+b=13$
Image
If $a=4$ and $c+b=4$, then $b+c=4$ and $a+a=c\Rightarrow c=8$
But then $b+c$ can't be $4$
So $a=3$ and $c+b=13$
Tens column is $b+c+1=14$
Hundreds column is $a+a+1=c $ so $c= 7$
So $b=6$ to make $c+b=13$