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

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

Archive

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