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24 Dec 2009

Square And Round Plugs      (24 Dec 2009)

Which fits better... a round plug in a square hole or a square plug in a round hole?

Irrationality Of Pi      (24 Dec 2009)

Prove that π is irrational.

30 Nov 2009

Inscribed Square      (30 Nov 2009)

Find the side length of the square inscribed inside the right angled triangle.

Algebraic Cosine      (30 Nov 2009)

Prove that cos(x) is algebraic if x is a rational multiple of Pi.

15 Nov 2009

3x3 Magic Square      (15 Nov 2009)

By considering rotations and reflections to be equivalent, prove that there exists only one 3x3 magic square.

Infinite Circles      (15 Nov 2009)

What fraction of the large red circle do the infinite set of smaller circles represent?

03 Nov 2009

Inscribed Circle In Right Angled Triangle      (03 Nov 2009)

Find the radius of the circle inscribed inside the right angled triangle.

Composite Fibonacci Terms      (03 Nov 2009)

Prove that for all composite values of n > 4, F_n is composite.

28 Oct 2009

Snapped Pole      (28 Oct 2009)

Can you determine the point where the pole snapped?

Bouncing Ball      (28 Oct 2009)

Where must the ball strike inside the square to return its point of origin?

11 Oct 2009

Net Perimeter      (11 Oct 2009)

By considering all the nets of a unit cube, which net has the greatest perimeter?

15 Degree Triangle      (11 Oct 2009)

Prove that the two smaller angles in the triangle are exactly 15^o and 75^o respectively.

27 Sep 2009

Unsorted Socks      (27 Sep 2009)

Find the minimum number of socks which must be taken from the drawers to be certain of finding five matching pairs.

Divisible By 99      (27 Sep 2009)

Find the smallest number made up of the digits 1 through 9 which is divisible by 99.

26 Aug 2009

Expressing Divisibility      (26 Aug 2009)

Prove that n(n + 1)(2n + 1) is divisible by six for all integer values, n.

Cuboid Perimeters To Volume      (26 Aug 2009)

Given the three perimeters of a cuboid can you determine its volume?

23 Jul 2009

Quarter Square      (23 Jul 2009)

How many ways can exactly two quarter squares be shaded?

Uninvited Guest      (23 Jul 2009)

Given that x² + x + 1 = 0, find the value of x³.

Fourth Power Plus Four Prime      (23 Jul 2009)

Given that n is a positive integer, when is n⁴ + 4 prime?

17 Apr 2009

Birds And Bunnies      (17 Apr 2009)

Can you find out how many birds are in the cage?