How to solve alphametic puzzles
- In many cases the result of an addition problem is one digit longer (in digit-length) than the addends – the numbers added. If there are only two addends, this implies that the extra digit is the number 1.
- In two addend alphametics, there may be columns that have the same letter in both the addends and the result. If such a column is the units column, that letter must be 0. Otherwise, it can either be 0 or 9 (and then there is a carry).
- If there are more than 2 addends, the same rules apply but need to be adjusted to accommodate other possibilities. If there are four identical letters in the units column (one of them the sum), this letter can now be: 0 or 5 (because 5+5+5=15). If there are four identical letters in a different column (one of them the sum), this letter can now be: 0 or 5 (no carry), 4 or 9 (carry 2). Four identical letters in a column other than the units column means a 1 could not have been carried over (why not?). This rule can be worked out for more than 3 addends as well…
- It is wise to turn subtraction problems into addition problems by adding the result to the smaller addend to get the larger one.
- When faced with a few options for a letter, try one out until you either get the correct answer, or find a contradiction.
Maths Puzzles: Cryptarithms, Symbologies and Secret Codes

Our purpose is to transform access to education.
We offer a diverse selection of courses from leading universities and cultural institutions from around the world. These are delivered one step at a time, and are accessible on mobile, tablet and desktop, so you can fit learning around your life.
We believe learning should be an enjoyable, social experience, so our courses offer the opportunity to discuss what you’re learning with others as you go, helping you make fresh discoveries and form new ideas.
You can unlock new opportunities with unlimited access to hundreds of online short courses for a year by subscribing to our Unlimited package. Build your knowledge with top universities and organisations.
Learn more about how FutureLearn is transforming access to education