Infinite Circles
What fraction of the large red circle do the infinite set of smaller circles represent? Problem ID: 367 (15 Nov 2009) / Difficulty: 4 star
View ArticleInscribed Square
Find the side length of the square inscribed inside the right angled triangle. Problem ID: 368 (30 Nov 2009) / Difficulty: 2 star
View ArticleAlgebraic Cosine
Prove that cos(x) is algebraic if x is a rational multiple of Pi. Problem ID: 369 (30 Nov 2009) / Difficulty: 4 star
View ArticleSquare And Round Plugs
Which fits better... a round plug in a square hole or a square plug in a round hole? Problem ID: 370 (24 Dec 2009) / Difficulty: 2 star
View ArticleIrrationality Of Pi
Prove that π is irrational. Problem ID: 371 (24 Dec 2009) / Difficulty: 4 star
View ArticleHops And Slides But Never Square
Prove that the minimum number of moves to completely reverse the positions of the coloured counters can never be square. Problem ID: 372 (07 Aug 2010) / Difficulty: 3 star
View ArticlePolynomial Roots
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. Problem ID: 373 (07 Aug 2010) / Difficulty: 3 star
View ArticleMultiplying Magic Square
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. Problem ID: 374 (16 Aug 2010) /...
View ArticleInscribed Circle In Isosceles Triangle
Find the radius of the circle inscribed inside the isosceles triangle. Problem ID: 375 (16 Aug 2010) / Difficulty: 2 star
View ArticleRectangle Construction
Find the connection between the constructed length and the original rectangle. Problem ID: 376 (17 Oct 2010) / Difficulty: 2 star
View ArticleIrrationality Of E
Prove that e is irrational. Problem ID: 377 (17 Oct 2010) / Difficulty: 4 star
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