
Reasoning, convincing and proving
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problemThe 30 students in a class have 25 different birthdays between them. What is the largest number that can share any birthday?
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problem
Wallpaper
These pieces of wallpaper need to be ordered from smallest to largest. Can you find a way to do it?
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problem
Trapezium four
The diagonals of a trapezium divide it into four parts. Can you create a trapezium where three of those parts are equal in area?
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problem
Domino sorting
Try grouping the dominoes in the ways described. Are there any left over each time? Can you explain why?
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problem
Product Sudoku
The clues for this Sudoku are the product of the numbers in adjacent squares.
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problem
Litov's mean value theorem
Start with two numbers and generate a sequence where the next number is the mean of the last two numbers...
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problem
Squares in rectangles
A 2 by 3 rectangle contains 8 squares and a 3 by 4 rectangle contains 20 squares. What size rectangle(s) contain(s) exactly 100 squares? Can you find them all?