# 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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cryptic clues factorials odd numbers lines fractions mean division functions wordplay unit fractions clocks money number chess cube numbers remainders multiples square numbers dates complex numbers probability advent multiplication shapes digits integers sum to infinity perfect numbers averages dodecagons factors area proportion christmas squares taxicab geometry percentages means ave square roots ellipses bases rectangles palindromes triangle numbers polygons indices cards sequences scales chocolate chalkdust crossnumber surds 3d shapes prime numbers time partitions books balancing calculus arrows 2d shapes symmetry circles differentiation irreducible numbers regular shapes crossnumbers games logic coins numbers addition spheres routes integration planes doubling geometry rugby trigonometry colouring pascal's triangle graphs people maths menace triangles speed floors perimeter folding tube maps crosswords star numbers shape grids coordinates algebra sport parabolas hexagons angles quadratics cryptic crossnumbers dice volume probabilty sums## 5 December

Today's number is the number of ways that 35 can be written as the sum of distinct numbers, with none of the numbers in the sum being divisible by 9.

Clarification: By "numbers", I mean (strictly) positive integers. The sum of the same numbers in a different order is counted as the same sum: eg. 1+34 and 34+1 are not different sums.
The trivial sum consisting of just the number 35 counts as a sum.