mscroggs.co.uk
mscroggs.co.uk

subscribe

Puzzles

9 December

The diagram below shows a rectangle. Two of its sides have been coloured blue. A red line has been drawn from two of its vertices to the midpoint of a side.
The total length of the blue lines is 50cm. The total length of the red lines is also 50cm. What is the area of the rectangle (in cm2)?

Show answer

8 December

Noel writes the numbers 1 to 17 in a row. Underneath, he writes the same list without the first and last numbers, then continues this until he writes a row containing just one number:
What is the sum of all the numbers that Noel has written?

Show answer & extension

Tags: numbers

7 December

There are 8 sets (including the empty set) that contain numbers from 1 to 4 that don't include any consecutive integers:
\(\{\}\), \(\{1\}\), \(\{2\}\), \(\{3\}\), \(\{4\}\), \(\{1,3\}\), \(\{1,4\}\), \(\{2, 4\}\)
How many sets (including the empty set) are there that contain numbers from 1 to 14 that don't include any consecutive integers?

Show answer & extension

Tags: number, sets

6 December

There are 5 ways to tile a 4×2 rectangle with 2×1 pieces:
How many ways are there to tile a 12×2 rectangle with 2×1 pieces?

Show answer

5 December

Put the digits 1 to 9 (using each digit exactly once) in the boxes so that the sums are correct. The sums should be read left to right and top to bottom ignoring the usual order of operations. For example, 4+3×2 is 14, not 10. Today's number is the product of the numbers in the red boxes.
++= 15
+ +
++= 15
+ × ÷
++= 15
=
15
=
15
=
15

Show answer

Tags: numbers, grids

4 December

If \(n\) is 1, 2, 4, or 6 then \((n!-3)/(n-3)\) is an integer. The largest of these numbers is 6.
What is the largest possible value of \(n\) for which \((n!-123)/(n-123)\) is an integer?

Show answer

3 December

190 is the smallest multiple of 10 whose digits add up to 10.
What is the smallest multiple of 15 whose digits add up to 15?

2 December

Holly adds up the first six even numbers, then adds on half of the next even number. Her total is 49.
Next, Holly adds up the first \(n\) even numbers then adds on half of the next even number. This time, her total is 465124. What is \(n\)?

Show answer & extension

Archive

Show me a random puzzle
 Most recent collections 

Advent calendar 2024

Advent calendar 2023

Advent calendar 2022

Advent calendar 2021


List of all puzzles

Tags

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

Archive

Show me a random puzzle
▼ show ▼
© Matthew Scroggs 2012–2025