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Hadamard's maximum determinant problem asks to find the largest possible determinant (in absolute value) for any n×n matrix whose elements are taken from some set. Hadamard ...

Given five equal disks placed symmetrically about a given center, what is the smallest radius r for which the radius of the circular area covered by the five disks is 1? The ...

Place a point somewhere on a line segment. Now place a second point and number it 2 so that each of the points is in a different half of the line segment. Continue, placing ...

What is the longest ladder that can be moved around a right-angled hallway of unit width? For a straight, rigid ladder, the answer is 2sqrt(2), which allows the ladder to ...

Let four lines in a plane represent four roads in general position, and let one traveler T_i be walking along each road at a constant (but not necessarily equal to any other ...

Given a circular table of diameter 9 feet, which is the minimal number of planks (each 1 foot wide and length greater than 9 feet) needed in order to completely cover the ...

What is the sofa of greatest area S which can be moved around a right-angled hallway of unit width? Hammersley (Croft et al. 1994) showed that S>=pi/2+2/pi=2.2074... (1) ...

Find a way to stack a square of cannonballs laid out on the ground into a square pyramid (i.e., find a square number which is also square pyramidal). This corresponds to ...

Given a unit disk, find the smallest radius r(n) required for n equal disks to completely cover the unit disk. The first few such values are r(1) = 1 (1) r(2) = 1 (2) r(3) = ...

Given three coins of possibly different sizes which are arranged so that each is tangent to the other two, find the coin which is tangent to the other three coins. The ...