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 2020

Advent calendar 2019

Sunday Afternoon Maths LXVII

Coloured weights
Not Roman numerals

Advent calendar 2018


List of all puzzles

Tags

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

Archive

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