mathschallenge.net

Rectangle Construction      Problem ID: 376 (17 Oct 2010)

Find the connection between the constructed length and the original rectangle.

Irrationality Of E      Problem ID: 377 (17 Oct 2010)

Prove that $e$ is irrational.

Inscribed Circle In Isosceles Triangle      Problem ID: 375 (16 Aug 2010)

Find the radius of the circle inscribed inside the isosceles triangle.

Multiplying Magic Square      Problem ID: 374 (16 Aug 2010)

Show how the values 1, 2, 4, 8, 16, 32, 64, 128, and 256 can be placed in a 3x3 square grid so that the product of each row, column, and diagonal gives the same value.

Polynomial Roots      Problem ID: 373 (07 Aug 2010)

Prove that the roots of the polynomial, $x$ⁿ + $c$_n-1$x$^n-1 + ... + $c$₂$x$² + $c$₁$x$ + $c$₀ = 0, are irrational or integer.

Hops And Slides But Never Square      Problem ID: 372 (07 Aug 2010)

Prove that the minimum number of moves to completely reverse the positions of the coloured counters can never be square.

Square And Round Plugs      Problem ID: 370 (24 Dec 2009)

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

Irrationality Of Pi      Problem ID: 371 (24 Dec 2009)

Prove that π is irrational.

Inscribed Square      Problem ID: 368 (30 Nov 2009)

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

Algebraic Cosine      Problem ID: 369 (30 Nov 2009)

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

3x3 Magic Square      Problem ID: 366 (15 Nov 2009)

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

Infinite Circles      Problem ID: 367 (15 Nov 2009)

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

Inscribed Circle In Right Angled Triangle      Problem ID: 364 (03 Nov 2009)

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

Composite Fibonacci Terms      Problem ID: 365 (03 Nov 2009)

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

Snapped Pole      Problem ID: 362 (28 Oct 2009)

Can you determine the point where the pole snapped?

Bouncing Ball      Problem ID: 363 (28 Oct 2009)

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

Net Perimeter      Problem ID: 360 (11 Oct 2009)

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

15 Degree Triangle      Problem ID: 361 (11 Oct 2009)

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

Unsorted Socks      Problem ID: 358 (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      Problem ID: 359 (27 Sep 2009)

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