mscroggs.co.uk
mscroggs.co.uk

subscribe

Advent calendar 2016

20 December

Earlier this year, I wrote a blog post about different ways to prove Pythagoras' theorem. Today's puzzle uses Pythagoras' theorem.
Start with a line of length 2. Draw a line of length 17 perpendicular to it. Connect the ends to make a right-angled triangle. The length of the hypotenuse of this triangle will be a non-integer.
Draw a line of length 17 perpendicular to the hypotenuse and make another right-angled triangle. Again the new hypotenuse will have a non-integer length. Repeat this until you get a hypotenuse of integer length. What is the length of this hypotenuse?

Archive

Show me a random puzzle
 Most recent collections 

Advent calendar 2025

Advent calendar 2024

Advent calendar 2023

Advent calendar 2022


List of all puzzles

Tags

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

Archive

Show me a random puzzle
▼ show ▼
© Matthew Scroggs 2012–2026