# Puzzles

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#### Sunday Afternoon Maths LXVII

Coloured weightsNot Roman numerals

#### Advent calendar 2018

#### Sunday Afternoon Maths LXVI

Cryptic crossnumber #2#### Sunday Afternoon Maths LXV

Cryptic crossnumber #1Breaking Chocolate

Square and cube endings

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In September, my puzzle appeared as Alex Bellos's Monday Puzzle. The puzzle asked what the highest rugby score was which can only be made with one combination of kicks, tries and converted tries.

What is the highest rugby score which can be made with 101 different combinations of kicks, tries and converted tries?

## Shooting hoops

Source: Alex Bolton

You spend an afternoon practising throwing a basketball through a hoop.

One hour into the afternoon, you have scored less than 75% of your shots. At the end of the afternoon, you have score more than 75% of your shots.

Is there a point in the afternoon when you had scored exactly 75% of your shots?

## Rugby scores

In a rugby (union) match, 3 point are scored for a kick, 5 for a try and 7 for a converted try. This scoring system means that some total scores can be achieved in different combinations, while others can be achieved in only one way.

For example, 14 can be scored in two ways (three kicks and a try; or two converted tries), while 8 can only be achieved in one way (try and a kick).

What is the highest score which can only be made in one way?

What is the highest score which can be made in two ways?

## Tennis

What is the minimum number of times a player has to hit the ball in a set of tennis and win a standard set (the set is not ended by injury, disqualification, etc.)?