Arrange seven points in a plane puzzle
PuzzlesIs it possible to arrange seven points in a plane so that any subset of three points will contain at [...]
Sum of the squares of consecutive Fibonacci numbers puzzle
PuzzlesThe first few Fibonacci numbers are 1, 1, 2, 3, 5, 8, 13, 21, 34, … (each number is the [...]
Arrange four distinct points puzzle
PuzzlesIn how many ways can you arrange 4 distinct points in the plane so there are exactly two different distances [...]
Perfect squares and perfect cubes puzzle
PuzzlesEach of the 12 white squares is to be filled with a single digit. The four 2 digit numbers and [...]
Greek crosses puzzle
Puzzles
A square can be cut into six pieces that can then be arranged to form two different Greek crosses as […]
Three circles in a triangle puzzle
Puzzles
In an equilateral triangle with side length 1 what is the largest area that can be covered by three non-overlapping […]
Find the number A puzzle
PuzzlesThe number B is obtained by removal of the last digit of the four-digit number A. Given A + B [...]
Sequence of positive integers puzzle
Puzzles
Let xn be a sequence of positive integers satisfying x1 = 4, x2 = 6 and xn + 1 is […]
Right-angled triangle puzzle
Puzzles
In the right-angled triangle below, a and b are integers and b < 2010. Find a and b. Right-angled triangle […]
Area of circle outside of the square
Puzzles
In the diagram the circle and square have the same centre and the same perimeter. What fraction of the area […]