Peter Zimmerman, a Year 13 student at Mill Hill County High School
in Barnet, London wrote this account of modulus arithmetic.
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.
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.
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?
Is this a fair game? How many ways are there of creating a fair
game by adding odd and even numbers?
Investigate powers of numbers of the form (1 + sqrt 2).
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?
A new card game for two players.
Follow-up to the February Game Rules of FEMTO.