Jack sells apples. He sells 12 apples the first day and 34 apples the
second day. After that each day he sells as many apples as he did the
previous two days combined. On what day will he first sell over 5,000
apples?
A bottle fully contains honey. The honey bottle weighed 1.5kg. Then the
bottle was weighed with half of the honey, it was 900 grams. How much
does the empty bottle weigh?
Alvin likes target shooting. He makes a bet with his friend Zeke. Each time Alvin makes a hit, Zeke has to pay
Alvin 10¢, but each time he misses Alvin has to pay Zeke 5¢. If Alvin shoots 30 times, and in the end he has to
pay Zeke 15¢, how many hits did he make?
There are 12 coins. One of them is
false; it has a different weight. It is
not known if the false coin is
heavier or lighter than the right
coins. How can you find the
suspicious coin by weighing on a
simple scale as few times as
possible?
A family of four is on one side of a rickety bridge across a
deep and otherwise uncrossable chasm. They desperately
need to get to the other side. Perhaps they are being
pursued by monsters. I don’t know. But I do know that it’s
night time–totally dark, no moon. The bridge can only
support the weight of two people at any given time, and it
doesn’t have a hand rail or anything like that, so you could
walk right off the edge if you can’t see where you’re
going. So anyone who is on the bridge had better have a
flashlight with them.
Our family of four has a flashlight. Just one, though, and
the batteries are dying. In fact, there are only 17 minutes
of battery power left. The family knows that it will take
Grandma 10 minutes to cross the bridge. Dad will need 5
minutes, little Pokey will take 2 minutes, and Speedy will
take 1 minute to cross. If two people are on the bridge
together, they will have to travel at the rate of the slower
person, because they have to share the flashlight.
There is no funny stuff, like throwing the flashlight (or
throwing Grandma) across. Can you save this family by
telling them how to get across in 17 minutes or less?
If a certain number is divided by 12, the quotient,
dividend, and divisor will have a sum of 64. What is
the number?
It takes 1629 digits to
number the pages of a
book. How many pages
does the book have?
In a family with 4 siblings, John is older than
Mary, Peter is younger than John, Mary is older
than Peter, and Sarah is older than John. Who is
the second oldest in the family? Who is the
youngest?
Use four 5’s and some of the symbols +, ×, −, and ÷ to give expressions
for 0, 1, 2, and 5 (You don’t need to use all the operation symbols in each
expression, but you must use 4 5’s.)
The Hilbert Hotel in the town of
Aleph has infinitely many rooms.
One night Mr. Cantor is driving
through Aleph when his car breaks
down. All the repair shops are
closed, so he needs a room for the
night. When he goes to the Hilbert
Hotel to check in, the desk clerk
tells
him that all the rooms are full. However, since there are infinitely many rooms, after thinking a bit, the clerk
manages to find a way to free up a room for Mr. Cantor. How does he do this?
You have found a mutant algae that doubles in
size every hour. It takes 18 hours for one algae
plant to take up half of a certain lake.
A octopus has 8 legs. A hippogriff has 6 legs and 2 pairs of wings.
A sphinx has 6 legs and one pair of wings. Now we have all 3
kinds and a total of 18 insects in a cage. We have a total of 118
legs and 20 pairs of wings. How many do we have of each kind ?