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# Maths Week: Your Saturday puzzle

Fancy a mathematics challenge?

MATHS WEEK STARTS today and, as is our annual tradition, we’re setting our readers some puzzles. Give them a go!

Day One – A Birthday Match

The Irish rugby squad has two players who share a birthday. What are the chances of that?

This is known as the Birthday Paradox as the answer is quite surprising – largely because our brains aren’t well evolved to assess probabilities. Probability itself is a relatively recent branch of maths dating back to the 17th Century (more about this later in the week).

How many people would we have to have in a room to have a 100% chance of two people sharing a birthday?

There are 365 days in a year, or 366 in a leap year. Therefore, we could have 366 people in a room who all have different birthdays. If one more person walked into the room, we would have to have a birthday match. That is 367 people to be 100% sure of having at least one matching birthday.

A much more difficult question is, how many people would we have to have in a room to have a 50:50 chance of two people sharing a birthday? So, if 367 are needed to be 100% certain of a matching birthday, might we need half of that number to have a 50% chance? Would that be 183 people?

The answer is rather surprising at 23 people. One of the reasons we find it surprising is that we might be thinking of ourselves and the chance of somebody sharing a birthday with us. The chance of a person walking into a room of 22 other people and finding a birthday that matches their own is much smaller and is about 6%. In a typical school with an average class size of 25 pupils you would expect around half the classes to contain a matching birthday.

In the Irish rugby squad, there are 33 players and the probability of finding a matching birthday is a little over 75%. The probability in the starting 15 would be around a 25%, but it just happens that the two players sharing a birthday are named in the starting line-up today and they are Peter O’Mahony and Dan Sheehan who blow out the candles on 17 September each year.

Each day, for Maths Week, The Journal will be bringing you fun puzzles. For many of these, we’ll be drawing on classic puzzles where today’s one comes from 1963 and the pen of the legendary recreational maths author, Martin Gardner.

So, here we go:

When I asked her how old she was, she smiled and said cryptically, “The day before yesterday I was 22, but next year I’ll be 25.”

Can you explain how this could be?

Come back tomorrow at 7.30pm for the answers to today’s puzzle.

The puzzles this week have been compiled by Eoin Gill and Colm Mulcahy of Maths Week Ireland / South-East Technological University (SETU).

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The Journal Team