1. A man has 53 socks in his drawer: 21 identical blue, 15 identical black and 17 identical red. The lights are fused and he is completely in the dark. How many socks must he take out to make 100 per cent certain he has a pair of black socks?

2. In a party of 35 people there are twice as many women as children and twice as many children as men. How many of each are there?

**ANSWERS:**

**40 socks.**

**SOLUTIONS:****If he takes out 38 socks, although it is very unlikely, it is possible they could all be blue and red. To make 100 percent certain that he also has a pair of black socks he must take out a further two socks.**

2. In a party of 35 people there are twice as many women as children and twice as many children as men. How many of each are there?

**ANSWERS:**

**5 men, 10 children and****20 women**.**SOLUTIONS:**
IF x = the number of men,

then x + 2x + 4x = 35.

Therefore 7x = 35.

So X = 5.

then x + 2x + 4x = 35.

Therefore 7x = 35.

So X = 5.

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