mscroggs.co.uk
mscroggs.co.uk

subscribe

Puzzles

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.

15 December

Today's number is smallest three digit palindrome whose digits are all non-zero, and that is not divisible by any of its digits.

Show answer

13 December

There is a row of 1000 lockers numbered from 1 to 1000. Locker 1 is closed and locked and the rest are open.
A queue of people each do the following (until all the lockers are closed):
Today's number is the number of lockers that are locked at the end of the process.
Note: closed and locked are different states.

Show answer

7 December

There is a row of 1000 closed lockers numbered from 1 to 1000 (inclusive). Near the lockers, there is a bucket containing the numbers 1 to 1000 (inclusive) written on scraps of paper.
1000 people then each do the following:
Today's number is the number of lockers that will be closed at the end of this process.

Show answer

6 December

This puzzle is inspired by a puzzle that Daniel Griller showed me.
Write down the numbers from 12 to 22 (including 12 and 22). Under each number, write down its largest odd factor*.
Today's number is the sum of all these odd factors.
* If a number is odd, then its largest odd factor is the number itself.

Show answer

Digitless factor

Ted thinks of a three-digit number. He removes one of its digits to make a two-digit number.
Ted notices that his three-digit number is exactly 37 times his two-digit number. What was Ted's three-digit number?

Show answer & extension

Archive

Show me a random puzzle
 Most recent collections 

Advent calendar 2019

Sunday Afternoon Maths LXVII

Coloured weights
Not Roman numerals

Advent calendar 2018

Sunday Afternoon Maths LXVI

Cryptic crossnumber #2

List of all puzzles

Tags

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

Archive

Show me a random puzzle
▼ show ▼
© Matthew Scroggs 2012–2020