These puzzles require only simple logic and elementary math.
We will list the names of anyone who solves the problems
marked with a *.
Two Trains
Trains travel from Foodletown to Myerville all day, always on the
same track, always going nonstop and at the same speed. The noon
train took 80 minutes to complete the trip, but the 4 PM train
took an hour and 20 minutes. Why?
Answer
Cube
It is easy to cut a 3×3×3 wooden cube into 27 little cubes
using 6 cuts. If you are allowed to rearrange the pieces after each cut,
what is the smallest possible number of cuts?
Answer
Wine & Water
There is a cask of wine, and a larger barrel of water. I take a dipper
of wine and add it to the water. Then I take a dipper of the water/wine
mixture and pour it back into the wine barrel.
Is there now more wine in the water, or more water in the wine?
Answer
Flurp
The game of Flurp is played on a square board measuring 10 inches by 10 inches.
The game uses 50 playing tiles each measuring 1 inch by 2 inches. There are
more than 100 million different ways to cover the board using these tiles.
Suppose that you cut out a 1 inch square from the upper left and lower right
corners of the board. Show that it is not possible to cover the board using
49 of the playing tiles.
Answer
Flags
The great square fortress Fua stands on the level Dal Mahir plain where
the straight east-west and north-south roads meet. Along the tops of
the outer fortress walls there are flags on short flagpoles, such that a
traveler approaching the fortress by road from any direction sees 3 flags.
(It is not possible to see a flag which is not on a wall that you are
facing directly.)
How many flags are there altogether? You should give the smallest
number possible.
Answer
Backgammon
103 backgammon players gather for a 7-round elimination tournament. How many
games are needed to determine a single winner?
Answer
Trip
Judy drives 107 miles from Fayer to Blungit averaging 30 miles per hour.
How fast must she drive on the return trip to average 60 mph overall?
Answer
Hey, Hay
If 6 horses eat 6 bales of hay in 6 days, how many bales will
12 horses eat in 12 days?
Answer
Fishing Rod
Little Jenny just bought a 5-foot fishing rod. The store put it in a
tubular package, slightly more than 5 feet long. She stepped on the bus
to go home, but the driver said that you are not allowed to bring any
package on the bus that measures more than 3 feet in any direction.
Jenny went back in the store, and a few minutes later got on the bus
and went home with her fishing rod. What did she do in the store?
Answer
* Sliding Coins
Below are pictured 5 coins (represented by X and O). Your job is
to get the 3 X's together and the 2 O's together by sliding the
coins. You must slide two coins at a time, an X and an O. They
must start adjacent to each other, and must end adjacent to each other. They
must move together as a unit. You cannot move them further apart or closer
together, and you cannot turn them around, that is turn XO into OX
or OX into XO. You also cannot spread the 3 remaining coins
apart or push them closer together. The coins must end up in a straight line
with no gaps.
It can be done in just 4 moves. Can you find them?
X O X O X
Solved by: Lars-Ake Aspelin, Glenn C. Rhoads,
Clarence Robinson Jr., Michael Dufour, S. Yap, Solenne Bourguin, Gilles Ravat,
Chris Schumann, Neeraj Parik, Gaurav Jain, Nitin Agrawal, Jean-Charles
Meyrignac, J. Michael Anderson, Amitayu Pal, Ritwik Chaudhuri, Sudipta Das,
Nick McGrath, Bappaditya Banerjee, Andrew Simon, Andreas Abraham,
Toby Gottfried, Janaki Mahalingam, Taylor Freeman, Sujay Shastry,
Aaron Weiner, Michael Mendelsohn, Yuval Bental, Joe Palmieri,
Pete Wiedman, P.M.A. Hakeem
Smith & Jones
How many people must there be if all but 2 are named Smith,
all but 2 are named Jones, and all but 2 are named Wilson?
Answer
Barrel
Two people agree to share a full barrel of wine. They have a dipper to
transfer the wine, and a somewhat smaller second barrel for the other share.
How can they share it evenly?
Answer
* The Chain
A blacksmith has 10 scrap pieces of chain that he wants to join
together to make a whole chain. It takes time to open and reweld a link,
so he wants to do this as few times as possible. The number of links
in the scraps are 2, 3, 4, 6, 8, 9, 12, 13, 15 and 19.
What is the most efficient way for him to join all the pieces?
Solved by: Guy Galan, Gregg Weimer, Hareendra Yalamanchili,
David Newell, Adela Garcia, Vivek Narayanan, Joakim Botterli, Gary Witt,
Pete Wiedman, Alan Day, P.M.A. Hakeem, Delmar Fenn
Bookworm
The 10 volumes of an encyclopedia are arranged in order, left to right,
on a shelf. A bookworm eats its way through, starting
at page 1 of volume 1 and going by the most direct route through
the last page of volume 10. Each cover is 5mm thick, and the pages
in each volume are 60mm thick. How far will the bookworm travel?
Answer
Horserace
The old king is dying, and wants to leave his kingdom to the wiser of
his two sons. He tells them that he will hold a horserace, and the son
whose horse is the last to reach the bridge and come back will inherit
the realm. Immediately the younger son jumps on a horse and makes for
the bridge at top speed. The king now knows that this is the wiser son,
and leaves him the kingdom. Why?
Answer
Windows
I have 2 windows in the front of my house. Each window is square,
4 feet high and 4 feet wide. But one window is twice as large
as the other. How is this possible?
Answer
2 Coins
I have 2 coins in my hand that add up to 30 cents, however one of them
is NOT a quarter. They are common U.S. coins. What are they?
Answer
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