8,292,015 is a composite, deficient, odd, odious and wasteful number. When written in base 36 it is 4XQ5R. And, it can be expressed as the sum of all of the integers from 3741 to 5529.
Another puzzle from “Amusements in
Mathematics” by Henry Dudeney.
“In this case I give a rough plan of a
river with an island and five bridges.
On one side of the river is a monastery, and on the other side of the
river is seen a monk in the foreground.
Now, the monk has decided that he will cross every bridge once, and only
once on his return to the monastery.
This is, of course, quite easy to do, but on the way he thought to
himself, “I wonder how many different routes there are fom which I might have
selected.” Could you have told him? That is the puzzle. Take your pencil and trace out a route that
will take you once over all five
bridges. Then trace out a second route,
then a third, and see if you can count all of the variations. You will find that the difficulty is two
fold: you have to avoid dropping routes on the one hand and counting the same
route more than once on the other.”
David
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