An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
A circle is inscribed in an equilateral triangle. Smaller circles touch it and the sides of the triangle, the process continuing indefinitely. What is the sum of the areas of all the circles?
Rectangle PQRS has X and Y on the edges. Triangles PQY, YRX and XSP have equal areas. Prove X and Y divide the sides of PQRS in the golden ratio.
The Queen of Hearts has lost her tarts! She is sure that those knaves who have not eaten the tarts will tell her the truth and the guilty knave will tell lies. When questioned the five knaves declare:
Knave 1 One of us ate them
Knave 2 Two of us ate them
Knave 3 Three of us ate them
Knave 4 Four of us ate them
Knave 5 Five of us ate them
How many of the knaves were honest?
If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.
This problem is taken from the UKMT Mathematical Challenges.