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

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

Archive

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