## How was the party?

- How was the party?
- Great! You should have been there!
- Did many show up?
- That was one of the curious things.
- What was?
- We discovered that three of the people had birthday in the same month and on the same day of the week.
- So what?
- After having partied for a while my girl friend discovered that it was no coincidence.
- What was no coincidence?
- She demonstrated that we were the minimum number of people for that to happen.
- For what to happen?
- We were the minimum number of people so that one would be certain that three of us were born in the same month on the same day of the week.
- Maybe I didn’t miss a lot after all.

### 5 Responses to “How was the party?”

1. Richard Sabey Says:

There are 12 months and 7 days of the week. Thus if there are 2*12*7=168 people, there could be 2 born on every combination of month and day of week, so there must have been more than 168 people at the party, but with 169, by the pigeonhole principle, you were “the minimum number of people so that one would be certain that three of us were born in the same month on the same day of the week”.

2. Matt Campbell Says:

The problem essentially asks : “what are the minimum number of people so that one would be certain that three were born in the same month on the same day of the week?”
But this is a fallacy of probability. If by certain you really mean 100% likely. The answer is infinity.
Taking a simpler puzzle – let’s try “what are the minimum number of people so that one would be certain someone was born in December?” This answer would be the opposite (1-answer) of the probability that no one was born in December. About 11/12 for each person.
If there were 169 people at the party there would be a probability of 99.99996% that someone was born in December – but still not quite certain.

3. Chris Says:

You only require 3 people.

4. Chris Says:

Ooops, I got to smart for my own good. Allowing for leap years, you would need 2*366+1=733 people.

5. Chris Says:

Haste makes waste – I almost posted the correct solution at first, but thought I had a smart answer at the last second. Just too keen to see my name up in lights

The problem had nothing to do with probability. The people had to be carefully selected to provide the minimum possible number of people. If the people were randomly selected, then we’d have the infinity stuff to play with.

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