# Puzzles

## Archive

Show me a random puzzle**Most recent collections**

#### 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

List of all puzzles

## Tags

chocolate wordplay factors multiples perimeter algebra 3d shapes irreducible numbers surds cards volume doubling sums rectangles trigonometry ave calculus money grids books chalkdust crossnumber palindromes addition chess integers ellipses angles percentages geometry functions rugby arrows advent division number partitions taxicab geometry integration colouring square numbers circles people maths pascal's triangle shape menace hexagons probabilty graphs triangle numbers triangles scales balancing mean area perfect numbers proportion parabolas probability factorials averages multiplication differentiation quadratics lines clocks odd numbers complex numbers dice prime numbers square roots christmas cryptic crossnumbers polygons 2d shapes time spheres squares means sum to infinity unit fractions bases planes logic sport symmetry indices crossnumbers coordinates coins floors dates digits games remainders numbers fractions regular shapes folding tube maps cube numbers routes speed sequences star numbers crosswords cryptic clues shapes dodecagons## 7 December

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?

## 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?