Prize Puzzle Competition 27

Closing date is 28th February 2001

79. The year 2001 starts at the midnight which falls between 31st December 2000 and 1st January 2001.
As the millionth second following the start of 2001 comes up,
what will be the day, date and time?

80. The drawing shows a chain of five gear-wheels, identified as A to E, each one meshing properly with its immediate neighbour(s). The number under each one show how many teeth that particular gear-wheel has.
Gear Wheel Train
When A is turned clockwise ten full turns,
in which direction does E turn, and how many times?

81. A solid wooden cuboid is made which measures an exact, and even, number of centimetres along each of its edges.
It is then painted black all over its exposed faces and, when the paint is dry, the cuboid is cut up into 1 centimetre cubes.
These small cubes are counted and it is then found that the number having NO paint on them at all, is exactly the same as the number which do have some paint on them.
What is the LEAST number of small cubes there could be in total?

The winner of Competition #26 was Vicky Turnbull of Kinglassie, Fife.
The answers were:

76.Some possibilities are 'pace' (or 'cape') 'area' 'gale' 'bend'
together with 'caged' (or 'cadge') and 'faded'.
77.The last digit is 5
The TOTAL is 264 - 1
and 264 = 18 446 744 073 709 551 616
78.0.2677 km   129920 mm   234.06 metres
Other answers are possible by selecting the appropriate SI prefixes.