mscroggs.co.uk
mscroggs.co.uk

subscribe

Puzzles

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

20 December

The integers from 2 to 14 (including 2 and 14) are written on 13 cards (one number per card). You and a friend take it in turns to take one of the numbers.
When you have both taken five numbers, you notice that the product of the numbers you have collected is equal to the product of the numbers that your friend has collected. What is the product of the numbers on the three cards that neither of you has taken?

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

Backwards fours

If A, B, C, D and E are all unique digits, what values would work with the following equation?
$$ABCCDE\times 4 = EDCCBA$$

Show answer

10 December

How many zeros does 1000! (ie 1000 × 999 × 998 × ... × 1) end with?

Show answer

17 December

In March, I posted the puzzle One Hundred Factorial, which asked how many zeros 100! ends with.
What is the smallest number, n, such that n! ends with 50 zeros?

One hundred factorial

How many zeros does \(100!\) end with?

Show answer & extension

Archive

Show me a random puzzle
 Most recent collections 

Advent calendar 2020

Advent calendar 2019

Sunday Afternoon Maths LXVII

Coloured weights
Not Roman numerals

Advent calendar 2018


List of all puzzles

Tags

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

Archive

Show me a random puzzle
▼ show ▼
© Matthew Scroggs 2012–2021