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

Day 3

If you were told there are two people in Dublin with the exact same number of hairs on their head, how would you confirm that?

We certainly don’t want to be going around counting hairs on heads, is there an easier way to answer this question?

Let’s look at a different question first. Assuming there are 10 pigeon holes (post boxes) in an office: If there are 11 letters delivered we know that at least one pigeon hole must receive more than one letter. This is known as the pigeon hole principle. 

Back to our hairy puzzle, what information would be helpful here? Google can help us. The CSO estimates the population of Dublin as 1.426 million. The number of hairs on the human head varies but the upper limit is typically around 150,000 hairs.

Assume that there are 150,000 people all with a different number of hairs on their head, from 1 hair to 150,000 hairs. Then the 150,001 person would have to have the same number of hairs as one of the preceding group.  So, in Dublin there must be at least two people with the exact same number of hairs on their heads. 

Now, figure this out:

1. You have only two colour socks, 6 black and 12 white. They are loose in a drawer. You pull them out without looking. How many socks do you have to withdraw to be certain of getting one pair?

2. One hundred mathematicians come to a meeting and naturally, they shake hands with others (or bump elbows of course but let’s stay traditional). Some are more friendly than others and will shake hands with more people. Can we be certain that at least two people shook hands with the same number of people?

3. You have 100 blue balls, 100 red balls and 100 yellow balls in a bag. How many balls would you have to pull out to be certain of getting 4 of one colour?

4. You draw cards at random from a standard deck (52 cards, 4 suits). What’s the maximum number of cards you would need to draw to be certain of getting 5 of one suit?

Come back tomorrow for the answer to today’s puzzle.

Puzzles compiled for TheJournal.ie by Eoin Gill of Maths Week Ireland / Waterford Institute of Technology

Sunday’s puzzle: The answers

Race finishing order:

1. Ciara

2. Dave

3. Anne

4. Emer

5. Bill

Houses:

1. Dearbhail, blue door

2. Bebhin, yellow door

3. Chris, pink door

4. Aine, green door

5. Eoghan, red door.

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