# Solving DEF+FEF=GHHDEF+FEF=GHH, KLM+KLM=NKLKLM+KLM=NKL, ABC+ABC+ABC=BBBABC+ABC+ABC=BBB

She visits third class and is $8$ years old (you can imagine how ashamed I felt when I said so to her). I helped her with lots of maths stuff today already but this is very unknowable for me. Sorry it’s in German but I have translated it 🙂

It’s saying “Each letter represents a digit. Determine them”. First question, what is “them”? The letters I guess?

How shall I determine them when they are unknown? Or is it simply $A=1, B=2, C=3, D=4, E=5, F=6, G=7, H=8, K=11, L=12, M=13, N=14$?

Alright…

With this we gave a) the first try:

It doesn’t seem to make sense to set $A=1, B=2, ...$

Or we did something wrong.. Any ideas how this could be solved? :s

1.This is a homework for a third grade girl, so we need to think as a kid but not as an advanced expert, in this case we will be able to explain to this kid step by step how we solve the problem and he will understand the solution in an easy way.

2.I do not think that the purpose of the teacher of a third grade was to make all letters equal to 0 because it will not make any sense to the children and they will not learn anything from this case, so I think that this is not a valid solution at all.

3.FYI: the solutions must be from right to left because this is how children learn to do calculations.

4.The three operations seems to be independents because they are no common letters between them.

5.I have started to solve the third operation (c):

The trick is to firstly we give the value 8 to C then we can find B because 8+8+8=24 which means we write 4 and we put 2 on the top of the second column. Therefore B = 4 then we replace B by 4 in the second column and in the result. In the second column we get 2+4+4+4=14 we write 4 and we put 1 on the top of the last column, in the last column we have the result 4 and we already have 1 on the top so A will be 1 (1+1+1+1=4)

SO A=1 ,B=4 ,C=8

6.For the second operation (b):

We give the value 1 to M then L= M+M = 1+1 = 2 so K = L+L = 2+2 = 4 in the end N = K+K = 4+4 = 8 therefore M=1, L=2, K=4, N=8 .Please notice if we give to M a value of 2,4,6,7,9 so the result will be on more then 3 digits (e.g. M=2 the result will be 1684) Therefore the solutions for M are 1,3,5,8.