# Chauffer problem

Sicilian Sausage
Posers and Puzzles 13 Sep '05 23:36
1. 13 Sep '05 23:36
A chauffer has 5 pairs of white gloves, 3 pairs of black gloves and 2 pairs of brown gloves in his draw. Without looking, how many gloves does he need to pull out of the draw to be sure he makes a complete pair?

ANd another one...

How many cards can be pulled out of a complete set of 52 playing cards, without having a full house combination?
2. PBE6
Bananarama
14 Sep '05 00:20
Originally posted by jimslyp69
A chauffer has 5 pairs of white gloves, 3 pairs of black gloves and 2 pairs of brown gloves in his draw. Without looking, how many gloves does he need to pull out of the draw to be sure he makes a complete pair?

ANd another one...

How many cards can be pulled out of a complete set of 52 playing cards, without having a full house combination?
OK:

(1) The chauffeur can pull out 5 lefty white gloves, 3 lefty black gloves and 2 lefty brown gloves. After that, the next glove will complete some pair, so the chauffer needs to pull out 5+3+2+1 = 11 gloves to be sure.

(2) A full house, consisting of one pair and one three of a kind, can be put off the longest by drawing a pair from each rank. After that, any card will complete some three of a kind making a full house. So the most cards that can be drawn without making a full house is 13*2 = 26 cards. The 27th card will make the full house.

Interesting questions. These are examples of problems that can be solved using the pigeonhole principle, a simple but powerful mathematical tool.
3. Bowmann
Non-Subscriber
14 Sep '05 18:29
In the chauffeur's sock drawer, he has a ratio of 5 pairs of blue socks, 4 pairs of brown socks, and 6 pairs of black socks...
4. 14 Sep '05 23:24
Originally posted by Bowmann
In the chauffeur's sock drawer, he has a ratio of 5 pairs of blue socks, 4 pairs of brown socks, and 6 pairs of black socks...
4
5. sonhouse
Fast and Curious
01 Oct '05 05:26
Originally posted by PBE6
OK:

(1) The chauffeur can pull out 5 lefty white gloves, 3 lefty black gloves and 2 lefty brown gloves. After that, the next glove will complete some pair, so the chauffer needs to pull out 5+3+2+1 = 11 gloves to be sure.

(2) A full house, consisting of one pair and one three of a kind, can be put off the longest by drawing a pair from each rank. Afte ...[text shortened]... lems that can be solved using the pigeonhole principle, a simple but powerful mathematical tool.
Please expand on the pigeonhole principle, never heard of it.
6. Bowmann
Non-Subscriber
19 Oct '05 15:12
Originally posted by sonhouse
Please expand on the pigeonhole principle, never heard of it.
Don't you get Google in Slatington?
7. royalchicken
CHAOS GHOST!!!
19 Oct '05 17:181 edit
Originally posted by sonhouse
Please expand on the pigeonhole principle, never heard of it.
Given two finite sets S and T, f: S->T is bijective if and only if card S = card T. In particular, if card T < card S, there must exist some t in T such that t = f(s1) and f(s2) for distinct s1, s2 in S.

A shavixmirian example: The average person has, I would guess, on the order of 10^5 pubes, and certainly nobody has more than 10^6 (I should hope). Since there are about 7*10^9 people in the world, the pigeonhole principle guarantees that there exist two people with the same number of pubes (this is an example of what's known as 'fuzzy logic' ðŸ˜‰).
8. PBE6
Bananarama
19 Oct '05 18:04
Originally posted by royalchicken
A shavixmirian example: The average person has, I would guess, on the order of 10^5 pubes, and certainly nobody has more than 10^6 (I should hope). Since there are about 7*10^9 people in the world, the pigeonhole principle guarantees that there exist two people with the same number of pubes (this is an example of what's known as 'fuzzy logic' ðŸ˜‰).
That's funny, I thought it was called the Crab Nebula. ðŸ˜•
9. sonhouse
Fast and Curious
19 Oct '05 20:17
Originally posted by Bowmann
Don't you get Google in Slatington?
too far out in the country, that plus terminal laziness.....