mscroggs.co.uk
mscroggs.co.uk

subscribe

Puzzles

11 December

Today's number is the number \(n\) such that $$\frac{216!\times215!\times214!\times...\times1!}{n!}$$ is a square number.

Show answer

Square and cube endings

Source: UKMT 2011 Senior Kangaroo
How many positive two-digit numbers are there whose square and cube both end in the same digit?

Show answer & extension

16 December

There are 204 squares (of any size) in an 8×8 grid of squares. Today's number is the number of rectangles (of any size) in a 2×19 grid of squares

14 December

There are 204 squares (of any size) in an 8×8 grid of squares. Today's number is the number of squares in a 13×13 grid of squares

What's the star?

In the Christmas tree below, the rectangle, baubles, and the star at the top each contain a number. The square baubles contain square numbers; the triangle baubles contain triangle numbers; and the cube bauble contains a cube number.
The numbers in the rectangles (and the star) are equal to the sum of the numbers below them. For example, if the following numbers are filled in:
then you can deduce the following:
What is the number in the star at the top of this tree?
You can download a printable pdf of this puzzle here.

Show answer

Square pairs

Source: Maths Jam
Can you order the integers 1 to 16 so that every pair of adjacent numbers adds to a square number?
For which other numbers \(n\) is it possible to order the integers 1 to \(n\) in such a way?

Show answer

Square factorials

Source: Woody at Maths Jam
Multiply together the first 100 factorials:
$$1!\times2!\times3!\times...\times100!$$
Find a number, \(n\), such that dividing this product by \(n!\) produces a square number.

Show answer & extension

Lots of ones

Is any of the numbers 11, 111, 1111, 11111, ... a square number?

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

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

Archive

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