Latest Problems


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, Fn 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 15o and 75o 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.