Concept 1 of 3
Cryptarithms: Letters Stand for Digits
Today's big idea
Each letter is one digit, the same every time, and no two letters may share a digit.
Each letter is one fixed digit; solve the column with the fewest choices first.
How it works
👀 What's going on?
A puzzle prints an addition with every digit replaced by a letter. Nothing about it is random. Exactly one set of digits makes the sum come out true, and the columns tell you where to start looking.
💡 Here's the trick
Each letter is one digit from 0 to 9. The same letter is always the same digit, and two different letters can never share one. Start where the choices are fewest rather than at the left. A carry can only ever add 1, so a letter leading the answer is almost always 1.
🪄 How to do it
- 1.Read the columns in the picture above and pick the one with the fewest choices.
- 2.Pin down a digit that makes that column end correctly.
- 3.Substitute it everywhere that letter appears, then move to the next column.
✍️ Try it
AB + BA = 121. What is A + B? And if A + A = B, with B still a single digit, what values can A take?
AB + BA is 11 lots of A + B, so A + B has to be 11. In the second, A + A must stay under 10. So A can be 1, 2, 3 or 4, making B 2, 4, 6 or 8.
⚠️ Watch out
Two different letters can never land on the same digit. An answer where the arithmetic works but two letters both come out as 4 is still wrong. Check every letter against the others before you commit.
🌟 Why this matters
Puzzle pages are full of these. The thinking is the same one you use to work out who did what from a handful of clues. You rule options out until only one of them can still be standing.
Exam tip: Write the digits 0 to 9 in a row and cross each one off as you place it. That is what stops two letters quietly sharing a digit.
Watch me solve one
Quanta solves it
“Watch how I think through one of these — then you try.”
THE PROBLEM
“If A + A = 14, find A.”
- 1
Translate
2A = 14
- 2
Divide
A = 14 ÷ 2 = 7
- 3
Answer ✓
A = 7
Now you try one — same steps, different story 👇
See it in action
⚡ Time to play!
Same letter = same digit. Start at the units column, work out the carry, then finish.
CRYPTARITHM · ROUND 1 OF 3
2 A + 4 8 = 7 3
Units: A + 8 ends in 3, so A = ?
Quick check
✅ VERIFICATION
A and B are single digits, A + B is a 2-digit number, and A = 1. What must B be?
⚡ Finish the activity above first to answer.
Keep going!
Up next: Multi-Step Unitary
Down to one, across to the other item, then up to the amount asked for.