Problems
Amazing Alphabet Maze
Stage:1 Challenge Level:
Can you go from A to Z right through the alphabet in the hexagonal maze?
A Flying Holiday
Stage:2 Challenge Level:
Follow the journey taken by this bird and let us know for how long and in what direction it must fly to return to its starting point.
The Moons of Vuvv
Stage:2 Challenge Level:
The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?
Making Mazes
Stage:2 Challenge Level:
What makes a maze harder to do? Make several mazes of the same size (you could do this with a group of maze-makers) and investigate which are the most difficult to do.
Delia's Routes
Stage:2 Challenge Level:
A little mouse called Delia lives in a hole in the bottom of a tree.....How many days will it be before Delia has to take the same route again?
A Calendar Question
Stage:2 Challenge Level:
July 1st 2001 will be on Sunday. July 1st 2002 will be on Monday. When will July 1st fall on a Monday again?
Networks and Nodes
Stage:2 Challenge Level:
Without taking your pencil off the paper or going over a line or passing through one of the points twice, can you follow each of the networks?
World of Tan - Almost There Now
Stage:2 Challenge Level:
Can you fit the tangram pieces into the outlines of the lobster, yacht and cyclist?
Number Daisy
Stage:2 Challenge Level:
Can you find six numbers to go in the Daisy from which you can make all the numbers from 1 to a number bigger than 35?
Triangular Triples
Stage:3 Challenge Level:
Show that 8778, 10296 and 13530 are three triangular numbers and that they form a Pythagorean triple.
Take Ten
Stage:3 Challenge Level:
Is it possible to remove ten unit cubes from a 3 by 3 by 3 cube made from 27 unit cubes so that the surface area of the remaining solid is the same as the surface area of the original 3 by 3 by 3. . . .
Mod 3
Stage:4 Challenge Level:
Prove that if a^2+b^2 is a multiple of 3 then both a and b are multiples of 3.
Root to Poly
Stage:4 Challenge Level:
Find the polynomial p(x) with integer coefficients such that one solution of the equation p(x)=0 is 1+sqrt2+sqrt3.
Long Short
Stage:4 Challenge Level:
A quadrilateral inscribed in a unit circle has sides of lengths s1, s2, s3 and s4 where s1 ≤ s2 ≤ s3 ≤ s4. Find a quadrilateral of this type for which s1= sqrt2 and show s1 cannot. . . .
Quadarc
Stage:4 Challenge Level:
Given a square ABCD of sides 10 cm, and using the corners as centres, construct four quadrants with radius 10 cm each inside the square. The four arcs intersect at P, Q, R and S. Find the. . . .
Iff
Stage:4 Challenge Level:
Prove that if n is a triangular number then 8n+1 is a square number. Prove, conversely, that if 8n+1 is a square number then n is a triangular number.
Parabolas Again
Stage:4 and 5 Challenge Level:
Here is a pattern composed of the graphs of 14 parabolas. Can you find their equations?
