In a land far, far away there lived a child named Euclid who loved to solve puzzles. One day Euclid was in a bakery and overheard the baker say that she needed exactly two cups of water for a recipe but only had a 3-cup measure and a 5-cup measure. Euclid took out a pad of paper and drew two cups, labeling the smaller one "3" and the larger one "5".

Euclid discovered that by filling up the "5" and pouring from it into the "3" until it was full, that exactly two cups of water would be left in the ''5". The baker thanked Euclid and gave Euclid a cookie.

During the following week, similar challenges were brought to Euclid. Can you help Euclid solve these?

Size of one measure | Size of the other measure | Exact amount of water needed | |
---|---|---|---|

1. | 2 cups | 7 cups | 3 cups |

2. | 3 cups | 7 cups | 5 cups |

Once you have solved each puzzle, try to find a second way to get the result.

Euclid claims that this third challenge is impossible

Size of one measure | Size of the other measure | Exact amount of water needed | |
---|---|---|---|

3. | 4 cups | 6 cups | 3 cups |

Can you find a way? If not, can you explain why it is impossible?

**Extension:** Make your own similar problems to solve with bigger numbers.