mscroggs.co.uk
mscroggs.co.uk

subscribe

Puzzles

24 December

There are six 3-digit numbers with the property that the sum of their digits is equal to the product of their digits. Today's number is the largest of these numbers.

Show answer

22 December

In bases 3 to 9, the number 112 is: \(11011_3\), \(1300_4\), \(422_5\), \(304_6\), \(220_7\), \(160_8\), and \(134_9\). In bases 3, 4, 6, 8 and 9, these representations contain no digit 2.
There are two 3-digit numbers that contain no 2 in their representations in all the bases between 3 and 9 (inclusive). Today's number is the smaller of these two numbers.

Show answer

17 December

Eve picks a three digit number then reverses its digits to make a second number. The second number is larger than her original number.
Eve adds her two numbers together; the result is 584. What was Eve's original number?

Show answer

1 December

If you write out the numbers from 1 to 1000 (inclusive), how many times will you write the digit 1?

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

22 December

In base 2, 1/24 is 0.0000101010101010101010101010...
In base 3, 1/24 is 0.0010101010101010101010101010...
In base 4, 1/24 is 0.0022222222222222222222222222...
In base 5, 1/24 is 0.0101010101010101010101010101...
In base 6, 1/24 is 0.013.
Therefore base 6 is the lowest base in which 1/24 has a finite number of digits.
Today's number is the smallest base in which 1/10890 has a finite number of digits.
Note: 1/24 always represents 1 divided by twenty-four (ie the 24 is written in decimal).

Show answer

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

9 December

Today's number is the number of numbers between 10 and 1,000 that contain no 0, 1, 2 or 3.

Show answer

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

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

Archive

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