mscroggs.co.uk
mscroggs.co.uk

subscribe

Puzzles

19 December

120 is the smallest number with exactly 16 factors (including 1 and 120 itself).
What is the second smallest number with exactly 16 factors (including 1 and the number itself)?

Show answer

2 December

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

Show answer

6 December

When 12345 is divided by today's number, the remainder is 205. When 6789 is divided by today's number, the remainder is 112.

Show answer

2 December

The number \(7n\) has 37 factors (including 1 and the number itself). How many factors does \(8n\) have?
There was a typo in this puzzle. It originally read "38 factors" when it was meant to say "37 factors".

Show answer & extension

15 December

When talking to someone about this Advent calendar, you told them that the combination of XMAS and MATHS is GREAT. They were American, so asked you if the combination of XMAS and MATH is great; you said SURE. You asked them their name; they said SAM.
Each of the letters E, X, M, A, T, H, S, R, U, and G stands for a different digit 0 to 9. The following sums are correct:
Today's number is SAM. To help you get started, the letter T represents 4.

Show answer

15 December

There are 5 ways to make 30 by multiplying positive integers (including the trivial way):
Today's number is the number of ways of making 30030 by multiplying.

Show answer

Not Roman numerals

The letters \(I\), \(V\) and \(X\) each represent a different digit from 1 to 9. If
$$VI\times X=VVV,$$
what are \(I\), \(V\) and \(X\)?

Show answer

20 December

Today's number is the sum of all the numbers less than 40 that are not factors of 40.

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

Archive

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