mscroggs.co.uk
mscroggs.co.uk

subscribe

Puzzles

16 December

Some numbers can be written as the sum of two or more consecutive positive integers, for example:
$$7=3+4$$ $$18=5+6+7$$
Some numbers (for example 4) cannot be written as the sum of two or more consecutive positive integers. What is the smallest three-digit number that cannot be written as the sum of two or more consecutive positive integers?

Show answer & extension

7 December

There are 8 sets (including the empty set) that contain numbers from 1 to 4 that don't include any consecutive integers:
\(\{\}\), \(\{1\}\), \(\{2\}\), \(\{3\}\), \(\{4\}\), \(\{1,3\}\), \(\{1,4\}\), \(\{2, 4\}\)
How many sets (including the empty set) are there that contain numbers from 1 to 14 that don't include any consecutive integers?

Show answer & extension

Tags: number, sets

2 December

What is the smallest number that is a multiple of 1, 2, 3, 4, 5, 6, 7, and 8?

Show answer

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.

Archive

Show me a random puzzle
 Most recent collections 

Advent calendar 2023

Advent calendar 2022

Advent calendar 2021

Advent calendar 2020


List of all puzzles

Tags

digits cubics matrices dates chocolate triangle numbers indices expansions albgebra products tournaments algebra balancing sums taxicab geometry remainders area people maths determinants the only crossnumber factorials volume square numbers floors combinatorics consecutive integers fractions unit fractions books complex numbers prime numbers sets games multiples functions rugby even numbers probability colouring proportion shape cryptic crossnumbers perfect numbers hexagons polygons clocks angles dodecagons quadratics rectangles shapes geometric mean probabilty digital products circles perimeter star numbers logic factors consecutive numbers squares geometric means mean symmetry 2d shapes spheres regular shapes square roots geometry multiplication cryptic clues arrows numbers dice ave integers chalkdust crossnumber crosswords integration coordinates binary elections pascal's triangle dominos lines routes grids differentiation bases 3d shapes coins gerrymandering polynomials money graphs scales wordplay tangents trigonometry christmas axes number parabolas sequences menace advent calculus chess crossnumbers triangles partitions median time averages crossnumber sum to infinity means doubling sport division irreducible numbers digital clocks pentagons decahedra odd numbers surds cube numbers range tiling quadrilaterals cards addition folding tube maps palindromes percentages speed ellipses planes

Archive

Show me a random puzzle
▼ show ▼
© Matthew Scroggs 2012–2024