# Course:CPSC312-2017-Math24 Solver Haskell

## Contents

## Math24 Solver

Authors: Lydia Li, Emrys Yang

### What is the problem?

The Math24 Game is an arithmetical card game in which the objective is to find a way to manipulate four integers so that the end result is 24. For example, for the card with the numbers 4, 7, 8, 8, a possible solution is (7 - (8 / 8)) * 4 = 24. We will attempt to generate a Math 24 game of simple difficulty using Haskell and see if Haskell can solve it (generate all possible solutions). For more information of Math24, see here: 24 Game

### What is the something extra?

- We will attempt to see if we can implement a 5-number version of Math24. This will allow people to insert 5 numbers and our Solver will also give out expressions consist with these 5 numbers, and get sum 24.

Example: (6 + 7 + 5 + 2 + 4) = 24 and (3 + 4 + 6 + 6 + 5) = 24.

- We will attempt to see if we can create a simplified solution so that same solution with different number order will be eliminated.

Example: (6 + 7 + 5 + 6) = 24 and (7 + 6 + 6 + 5) = 24 will be regarded as the same solution.

- We will attempt to see if we can create higher levels of difficulties for Math24 and have Haskell solve it too:

The original version of 24 is played with an ordinary deck of playing cards with all the face cards removed. The aces are taken to have the value 1 and the basic game proceeds by having 4 cards dealt and the player that can achieve exactly number 24 using allowed operations wins this round of the game.

Normally when we play this game, we only using basic operations (addition, subtraction, multiplication, division, and parentheses) to keep it simple and time-saving. However, in our Math24 Solver, we would like to include face cards (Jack = 11, Queen = 12, King = 13) and using more complex operations:

- Exponentiation.

Example: for cards 4, 2, 5, 3, we can do calculations like (4^2 + 5 + 3) = 24.

- Square Root. (Due to prolog language expression, sqrt() is same as
^{2}√, so card 2 is needed for this operation)

Example: for cards 4, 9, 2, 9, we can do calculations like (4 * (9 - sqrt(9))) = 24.

- Logarithms.

Example: for cards 4, 2, 10, 12, we can do calculations like (log_{2}(4) + 10 + 12) = 24.

- Factorial.

Example: for cards 3, 2, 6, 6, we can do calculations like (3! + 2 *6 + 6) = 24.