You have seven glasses on a table, all face down. You are allowed
to turn over four glasses at a time, as many times as you want. Is it possible
to end up with all seven glasses face up?
How can you distribute 127 single dollar bills among 7 wallets so that
any integer amount from 1 through 127 dollars can be paid without
opening the wallets?
A number of bacteria are placed in a glass. One second later each bacterium
divides in two, the next second each of the resulting bacteria divides
in two again, etc. After one minute the glass is full. When was the glass
half-full?
Let a1,a2,a3,...,an
represent an arbitrary arrangement of the
numbers 1,2,3,...,n. Show that, if n is odd, the product:
( a1 - 1 ) ( a2 - 2 ) ( a3 - 3 ) ... ( an - n )
is an even number.
Mary and Lucille live in two different towns, 50 miles apart.
They decided that they want to see each other. So, on Sunday at 10am
they take their bicycles and ride toward each other. Their speed is of 25mph.
At the same moment,(10am) Mary's pigeon starts flying toward Lucille. The pigeon flies
with 60mph. When it gets above Lucille it turns back and flies toward Mary. When it reaches her
it turns back and flies toward Lucille, etc. So at 11am all our three characters meet at half-distance.
What is the distance traveled by the pigeon?
You have 9 coins, one of which is counterfeit and weighs
less than the others. Use two weighings on a balance with two pans to
find the counterfeit coin.
Determine how many zeros end the number 100 ! .
(Hint: Remember that 100! = 100x99x98x...x2x1 .)