The children's game Hotter Colder is played as follows. Player A leaves the room while player B hides an object somewhere within. Player A re-enters at position (0, 0) and then visits various other locations about the room. When player A visits a new position,…

Little Tomy likes to cover his bread with milk. He does this by dipping it so that its bottom side touches the bottom of the cup, as in the picture below: <img src="/admin/../upload/pimg1605_1.png"> Since the amount of milk in the cup is limited, only th…

The Canadian Lumberjack Society has just held its annual woodcutting competition and the national forests between Montreal and Vancouver are devastated. Now for the social part! In order to lay out an adequate dance floor for the evening party the organizing c…

Ian is going to California and has to pack his things, including his collection of circles. Given a set of circles, your program must find the smallest rectangular box they fit in. All circles must touch the bottom of the box. The figure below shows an accepta…

The following figure shows a rectangular card of width W, length L, and thickness 0. Four x x x squares are cut from the four corners of the card shown by the dotted lines. The card is then folded along the dashed lines to make a box without a cover. <img s…

The image below shows a square ABCD, where AB = BC = CD = DA = a. Four arcs are drawn taking the four vertexes A, B, C, D as centers and a as the radius. The arc that is drawn taking A as center starts at neighboring vertex B and ends at neighboring vertex D. …