Overturning Fracsum

Solve the system of equations to find the values of x, y and z: xy/(x+y)=1/2, yz/(y+z)=1/3, zx/(z+x)=1/7

Bang's Theorem

If all the faces of a tetrahedron have the same perimeter then show that they are all congruent.

Rudolff's Problem

A group of 20 people pay a total of £20 to see an exhibition. The admission price is £3 for men, £2 for women and 50p for children. How many men, women and children are there in the group?

Weekly Problem 46 - 2006

Stage: 3 and 4 Challenge Level:

The standard Fibonacci sequence 1, 1, 2, 3, 5, 8, 13, ? begins with two 1s and each later number in the sequence is the sum of the previous two numbers. Other Fibonacci like sequences can be constructed by starting with any two numbers a and b (not necessarily 1 and 1) and using the same rule for creating the other numbers in the sequence. What is the first term of the Fibonacci-like sequence whose second term is 4 and whose fifth term is 22?

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.

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