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Resources tagged with Odd and even numbers similar to Modulus Arithmetic and a Solution to Differences:

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Broad Topics > Numbers and the Number System > Odd and even numbers

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Modulus Arithmetic and a Solution to Differences

Age 16 to 18

Peter Zimmerman, a Year 13 student at Mill Hill County High School in Barnet, London wrote this account of modulus arithmetic.

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Impossible Sandwiches

Age 11 to 18

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.

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Comparing Continued Fractions

Age 16 to 18 Challenge Level:

Which of these continued fractions is bigger and why?

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Summats Clear

Age 16 to 18 Challenge Level:

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.

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Reasonable Algebra

Age 14 to 16 Challenge Level:

Use algebra to reason why 16 and 32 are impossible to create as the sum of consecutive numbers.

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Lattice Points

Age 16 to 18 Challenge Level:

Why are there only a few lattice points on a hyperbola and infinitely many on a parabola?

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Prime Magic

Age 7 to 16 Challenge Level:

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?

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FEMTO: Follow Up

Age 14 to 16 Challenge Level:

Follow-up to the February Game Rules of FEMTO.

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FEMTO

Age 14 to 16 Challenge Level:

A new card game for two players.

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Bina-ring

Age 16 to 18 Challenge Level:

Investigate powers of numbers of the form (1 + sqrt 2).