Find the sum, f(n), of the first n terms of the sequence: 0, 1, 1,
2, 2, 3, 3........p, p, p +1, p + 1,..... Prove that f(a + b) - f(a
- b) = ab.
Peter Zimmerman, a Year 13 student at Mill Hill County High School
in Barnet, London wrote this account of modulus arithmetic.
Investigate powers of numbers of the form (1 + sqrt 2).
In this 7-sandwich: 7 1 3 1 6 4 3 5 7 2 4 6 2 5 there are 7 numbers between the 7s, 6 between the 6s etc. The article shows which values of n can make n-sandwiches and which cannot.
A new card game for two players.
Is this a fair game? How many ways are there of creating a fair
game by adding odd and even numbers?
Follow-up to the February Game Rules of FEMTO.
Use algebra to reason why 16 and 32 are impossible to create as the
sum of consecutive numbers.
Which of these continued fractions is bigger and why?
Why are there only a few lattice points on a hyperbola and
infinitely many on a parabola?
Place the numbers 1, 2, 3,..., 9 one on each square of a 3 by 3 grid so that all the rows and columns add up to a prime number. How many different solutions can you find?