Crossing a Bridge with only One Lantern
Four guys are attempting to cross over a chasm on a rickety old bridge
in the middle of the night. Because it is so dark, the bridge can only
be crossed with a lantern. Because the bridge is so unstable, only
two people can cross the bridge at a time.
The guys do have one lantern with them that will allow them to cross,
however, they are not all as nimble as each other. As a result, they
take different lengths of time to cross the bridge. The respective times
it takes for each to cross is 1min, 2min, 5min and 10min.
If two guys are walking across the bridge together with the lantern,
they can only cross as fast as the slower of the two can.
What order should they go in to get all four of the guys
across the bridge in the shortest total amount of time?
Laying Dominoes on a Chessboard
Assume you are placing dominoes on an 8x8 chessboard, such that each domino
will cover exactly two squares of the chessboard. Can you cover every square
of the chessboard with dominoes, without having any dominoes hanging off
the side of the board?
With a little thought, the answer to the above question should
obviously be "Yes." Now suppose, the two OPPOSITE corners of the
chessboard are removed.
Can the remaining 62 squares of the chessboard
be covered by dominoes without having any dominoes hanging off the board?