# Number Puzzle #19- The Five Thieves -

Five thieves were in a tavern and overheard a drunken shopkeeper bragging about his large collection of
diamonds. Later that night, one of the thieves broke into the shop. He had a bit of a conscience (as far
as thieves go) and only took half of the diamonds. But on his way out, he decided to take one more. After
all, he was a thief. A while later, the second thief arrived. It was a night of odd coincidences. He also
took half of the remaining diamonds plus one more. Shortly after, the third thief arrived and likewise
took half of the remaining diamonds plus one more. Next, the fourth thief arrived and he as well took
half of the remaining diamonds plus one more. Finally, the fifth thief arrived only to find that there
were no diamonds left. How many diamonds did the shopkeeper have at the start?

**HINT**: The trick is to work out the answer backwards (i.e. how many diamonds were
stolen by the fourth thief).

**ANSWER**:

*30.*
**EXPLANATION**: The trick is to work backwards. There were 0 diamonds left when the fifth
thief arrived. So that is how many diamonds remained after the fourth thief looted. Calculate the number
of diamonds that were there

*before* the fourth thief looted using: d - (d/2 + 1) = 0. Use this
same equation for the other thieves changing the 0 to the number of diamonds present when the
subsequent/later thief arrived.

Thief |
Diamonds after looting |
Diamonds before looting |

5 |
0 |
0 |

4 |
0 |
2 |

3 |
2 |
6 |

4 |
6 |
14 |

1 |
14 |
30 |

Do you have a

suggestion for this puzzle (e.g. something that should
be mentioned/clarified in the question or solution, bug, typo, etc.)?