mathschallenge.net

Irrationality Of E

Sun, 17 Oct 2010 00:00:00 +0000

Prove that e is irrational.

]]> Problem ID: 377 (17 Oct 2010) / Difficulty: 4 star

Rectangle Construction

Sun, 17 Oct 2010 00:00:00 +0000

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

]]> Problem ID: 376 (17 Oct 2010) / Difficulty: 2 star

Inscribed Circle In Isosceles Triangle

Mon, 16 Aug 2010 00:00:00 +0000

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

]]> Problem ID: 375 (16 Aug 2010) / Difficulty: 2 star

Multiplying Magic Square

Mon, 16 Aug 2010 00:00:00 +0000

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) / Difficulty: 3 star

Polynomial Roots

Sat, 07 Aug 2010 00:00:00 +0000

Prove that the roots of the polynomial, xⁿ + c_n-1x^n-1 + ... + c₂x² + c₁x + c₀ = 0, are irrational or integer.

]]> Problem ID: 373 (07 Aug 2010) / Difficulty: 3 star

Hops And Slides But Never Square

Sat, 07 Aug 2010 00:00:00 +0000

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

Irrationality Of Pi

Thu, 24 Dec 2009 00:00:00 +0000

Prove that π is irrational.

]]> Problem ID: 371 (24 Dec 2009) / Difficulty: 4 star

Square And Round Plugs

Thu, 24 Dec 2009 00:00:00 +0000

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

Algebraic Cosine

Mon, 30 Nov 2009 00:00:00 +0000

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

]]> Problem ID: 369 (30 Nov 2009) / Difficulty: 4 star

Inscribed Square

Mon, 30 Nov 2009 00:00:00 +0000

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

]]> Problem ID: 368 (30 Nov 2009) / Difficulty: 2 star

Infinite Circles

Sun, 15 Nov 2009 00:00:00 +0000

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

]]> Problem ID: 367 (15 Nov 2009) / Difficulty: 4 star