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

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

Archive

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