Maths: A coded sum

Just a note: I cracked this when I was twelve, but my father could not, even though his Bachelor of Arts included a major in philosophy.

Can you solve these coded sums? Each letter represents the same digit, each time.

If you can solve that puzzle yourself, you will probably get the puzzle above as well. It is a set of sums, coded so each number is replaced by a letter. I think I was 11 or 12 when I solved it because I knew it had to be solvable. Remember that, because it is the magic key. There is no sense in asking people to solve a problem that has no answer. Asking a question where you don’t know the answer is different. I do that all the time, but I always say when I don’t know!

Always start by knowing there has to be a way to solve a puzzle. Look at the addition at the top of the sum set above, and realise what the value of B is. Go down two sums to the multiplication and realise that D can only be zero, one, five or six, then rule out two of those right away. That’s all the help you get, for now.

Here is some help: use as much as you need, then jump back into the puzzle.

A simple example of a coded sum.

Let’s begin first with the simple puzzle above. If A+A = A in the first (right) column, then A = 0. If two four-digit numbers give a five-digit sum, E = 1. From the fourth (left) column, D+D = 10, so D = 5. From the second column, D= C+1, so C = 4, and from the third column, B = 2. So if we know a bit about numbers, these puzzles suddenly become a lot less tricky.

Now let’s look at the first part of the big sum. If you had x + y = x, what is the value of y? Look at the right-hand column below, and you will know that B is zero.

Starting the main puzzle.

In the hundreds column, B + D = F, but how can that be? Obviously there was a ‘carry’ from the tens column, so F is one more than D. All three rows have four numbers, so A has to be 1, 2, 3 or 4. I thought I would leave you to take it from there, but in the editing, I solved the puzzle again, and it was hard, so I decided to give you a bit more help:

This table shows how to start tackling it. In any row and column a y (for ‘yes’) means all the rest of that column or row is x, meaning ‘no’. The table below records my progress to the point where B is zero, A is 1, G is 2, F= D+1 and H=F-2=D-1. The rest is really up to you. If you can’t get there, set it aside. With codes and cryptic crosswords, you need to either own the right sort of mind, or grow the right sort of mind by practice. Let the puzzle marinate.

This is how I tackle problems like this.

Well, it's some help...

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