### Brain Teasers

# Billiards

In the old days of the Raj, the following conversation was heard:

'Hello, your name is Smythe isn't it? How about a friendly game of billiards?'

'Yes it is Colonel, I'm not very good though, Carstairs gives me a 25 point handicap when we play for 100 points.'

'Well, I'll just have to do better than that since I give Carstairs a 20-point handicap when I play him. Shall we play for £100 a game?'

How many points should Smythe be given as a handicap?

'Hello, your name is Smythe isn't it? How about a friendly game of billiards?'

'Yes it is Colonel, I'm not very good though, Carstairs gives me a 25 point handicap when we play for 100 points.'

'Well, I'll just have to do better than that since I give Carstairs a 20-point handicap when I play him. Shall we play for £100 a game?'

How many points should Smythe be given as a handicap?

### Answer

As the Colonel gives Carstairs 20 points in 100, he expects him to make 80 points by the time he reaches 100. Carstairs must shoot at a rate of 4/5 of the Colonel. As Smythe is expected to get 75 for every 100 Carstairs gets, he shoots at a rate of 3/4 of that of Carstairs.Smythe must shoot at a rate of 3/4 X 4/5 or 3/5 of that of the Colonel.

Smythe should be given a handicap of 40 points.

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