### Random Post

### Recent Posts

### Recent Comments

Jim Randell on Enigma 544a: Merry Christ… | |

Jim Randell on Puzzle #52: Bus change | |

J. Pijnenburg on Puzzle #52: Bus change | |

Jim Randell on Puzzle #53: Painting by n… | |

GeoffR on Puzzle #52: Bus change |

### Archives

### Categories

- article (11)
- enigma (1,367)
- misc (4)
- project euler (2)
- puzzle (90)
- puzzle# (48)
- site news (58)
- tantalizer (93)
- teaser (7)

### Site Stats

- 233,055 hits

Assuming each of the three pairs is distinguishable (perhaps each pair is a different colour), and all socks are washed together (6 in the first wash, 5 in the second wash, 4 in the third wash).

The first wash destroys one of the 6 socks. In the second wash there is a 4/5 chance that a different colour sock is destroyed. And in the third wash there is a 2/4 chance that one of the remaining pair will be destroyed.

The probability that three odd socks remain after the three washes is therefore: (4/5) × (2/4) = 2/5, or a 40% chance.

So there is a 60% chance that this doesn’t happen and one complete pair survives the first three washes.

It is probably better to buy three identical pairs of socks, and then you are guaranteed to have a usable pair after 3 (and even after 4) washes.