## Example rules

### Standard

Double the number and add two; eg 11 -> 24

Write the number in reverse; eg 13 -> 31

Write the number twice; eg 23 -> 2323

Count the number of characters in the word for the number; eg 21 -> 10

### Advanced

The number of the number's prime factors; eg 15 -> 2

The sum of the squares of the number's digits; eg 13 -> 10

The number written in base three; eg 26 -> 222

## Try and guess Eliza's rule

## Let Eliza guess your rule

### One player thinks of a mathematical rule and the other player tries to guess it. Play against our mathematical wizard Eliza!

# How to Play

## About the game

The Chooser thinks of a rule that converts one whole number (integer) into another. A mathematician would call this a "function".

The Guesser then tries to guess the rule by testing it with different numbers.

For example, if the Chooser thought of the rule "double it and add one", the game might proceed as follows:

- 1
- 3
- 2
- 5
- 10
- 21
- 100
- 201
- I think it's double it and add one
- Correct!

### Standard game

Rules can use arithmetic and everyday concepts.

### Advanced game

Rules can use mathematical concepts, including: squares, powers, bases, factors, divisors, modulo, prime numbers, and piecewise functions.

## Additional points

For some rules it may not be possible to give an answer for all guesses. For example, if the rule is "The number of times that the number divides into 100 (ignoring any remainder)", no answer is possible for the guess "0". In such cases the Chooser says "I can't answer it", or "Choose a larger number".

Some rules may have alternative ways of expressing them; for example "Add one and double it" is the same as "Double it and add two", which you can see by writing the rule as an equation:

(x+1) x 2 is the same as 2x+2.

Either of these is therefore a valid answer to this game. If there is any doubt the Chooser can give the Guesser a number to make sure they can arrive at the correct answer themselves.

## September 2023 Fiendish Function

Coming soon!## Last Month's Answer

Here is the answer to last month's Fiendish Function.