At the corner of the cube circular arcs are drawn and the area
enclosed shaded. What fraction of the surface area of the cube
is shaded? Try working out the answer without recourse to pencil
and paper. At the beginning of the night three poker players;
Alan, Bernie and Craig had money in the ratios 7 : 6 : 5. At the
end of the night the ratio was 6 : 5 : 4. One of them won $1
200. What were the assets of the players at the beginning of the
evening? According to Plutarch, the Greeks found all the
rectangles with integer sides, whose areas are equal to their
perimeters. Can you find them? What rectangular boxes, with
integer sides, have their surface areas equal to their volumes?