Working Systematically - Advanced
Binomial Coefficients
An introduction to the binomial coefficient, and exploration of some of the formulae it satisfies.
Pole Star Sudoku
A Sudoku based on clues that give the differences between adjacent cells.
Sorted
How can you quickly sort a suit of cards in order from Ace to King?
Difference Dynamics
Take three whole numbers. The differences between them give you three new numbers. Find the differences between the new numbers and keep repeating this. What happens?
Twin Chute-swapping Sudoku
A pair of Sudokus with lots in common. In fact they are the same problem but rearranged. Can you find how they relate to solve them both?
Constellation Sudoku
Special clue numbers related to the difference between numbers in two adjacent cells and values of the stars in the "constellation" make this a doubly interesting problem.
A Long Time at the Till
Try to solve this very difficult problem and then study our two suggested solutions. How would you use your knowledge to try to solve variants on the original problem?
Magic Caterpillars
Label the joints and legs of these graph theory caterpillars so that the vertex sums are all equal.
W Mates
Show there are exactly 12 magic labellings of the Magic W using the numbers 1 to 9. Prove that for every labelling with a magic total T there is a corresponding labelling with a magic total 30-T.
Function Pyramids
A function pyramid is a structure where each entry in the pyramid is determined by the two entries below it. Can you figure out how the pyramid is generated?
Twin Equivalent Sudoku
This Sudoku problem consists of a pair of linked standard Suduko puzzles each with some starting digits
Purr-fection
What is the smallest perfect square that ends with the four digits 9009?
Exhaustion
Find the positive integer solutions of the equation (1+1/a)(1+1/b)(1+1/c) = 2
Adding Machine
Can you set the logic gates so that this machine can decide how many bulbs have been switched on?
Impuzzable
This is about a fiendishly difficult jigsaw and how to solve it using a computer program.
Interpolating Polynomials
Given a set of points (x,y) with distinct x values, find a polynomial that goes through all of them, then prove some results about the existence and uniqueness of these polynomials.
Stage 5 Cipher Challenge
Can you crack these very difficult challenge ciphers? How might you systematise the cracking of unknown ciphers?
Knights Moving
Can you swap the black knights with the white knights in the minimum number of moves?