mscroggs.co.uk
mscroggs.co.uk

subscribe

Puzzles

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

Triangles between squares

Prove that there are never more than two triangle numbers between two consecutive square numbers.

Show answer & extension

Triangle numbers

Let \(T_n\) be the \(n^\mathrm{th}\) triangle number. Find \(n\) such that: $$T_n+T_{n+1}+T_{n+2}+T_{n+3}=T_{n+4}+T_{n+5}$$

Show answer & extension

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

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

Archive

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