Fill the square on the left with four red chips, four yellow chips, four
green chips and four blue chips so that no row, no column and none of the
two big diagonals have two chips of the same color. The four chips that
are already there can not be changed. Do the same with the square on the
right.
Put four copies of the A piece together to make exactly the same shape,
only bigger. Put four copies of the B piece together to make exactly the
same shape, only bigger. You are allowed to rotate the pieces and flip
them over but it is not allowed to overlap them.
Polyominoes are shapes that are made by joining identical squares along
their edges. A domino is a shape made from two identical squares. The
A-piece shown in the illustration is the only example of the domino. A
tromino is a shape made from three identical squares. There are only two
different trominoes – they are shown as two B-pieces above. A tetromino is
a shape made from four identical squares. Two tetrominoes shown as
C-pieces are really the same. If you cut them out or paper, they would be
exactly the same shape. Two different tetrominoes are shown as D-pieces in
the illustration. How many other different tetrominoes can you find? A
pentomino is a shape made from five identical squares. Two different
pentominoes are shown in the illustration as the couple of E-pieces. How
many other different pentominoes can you find?
This is a map of Circletown. Almost all of roads in Circletown are
circles. When you drive along a road in Circletown, you are not allowed to
do a U-turn, and you are not allowed to do a really sharp turn (the left
topmost diagram). Only smooth turns are allowed (the left bottom diagram).
Pat and Sandy are friends. Usually Sandy walks to Pat’s house, but today
Sandy will be driven to Pat’s house. The map shows where they live. Find a
route so that Sandy can visit Pat. The route must start at Sandy’s house
and end at Pat’s house, and you have to follow the rules.
Sammo the frog has to visit his doctor who lives on the white lilypad.
Sammo would like to hop right over there. He can hop back and forth along
the line of lilypads, but he was injured in a karate contest and can only
hop with one leg at a time. (That’s why he wants to see his doctor.) If he
hops with his right leg, he always lands exactly 11 lilypads away. If he
hops with his left he always lands exactly 7 lilypads away. As you can
see, his doctor’s lilypad is exactly 5 lilypads away. If he hops 11
forward and 7 backward, he just misses the doctor’s lilypad. How can Sammo
hop to his doctor’s lilypad?
A bookworm finds itself on page 1 of volume 1 and begins eating straight
through to the last page of volume 5. If each book is 6 centimeters thick,
including front and back covers, which are half a centimeter each, what is
the distance the bookworm travels?
Suppose you have six identical looking coins. Five weigh 8 grams, while
one weighs 7.9 grams. How can you identify the lighter coin in just two
weighings using a balance scale?
A large square can be quite easily divided into 4 identical sized smaller
squares. This is shown in the illustration. Obviously, all 4 smaller
squares are of the same size. There are 3 more ways to divide the large
square into 4 identically shaped parts. They are not squares, but each of
them must contain 4 mini squares. Can you find those 3 other ways?
It's possible to place six pencils on the table in such a way that every
of them touches the other two - as shown in the illustration. Can you
place the same six pencils on the table so that each pencil touches every
other one? Some readers of Martin Gardner's famous puzzle column in the
Scientific American magazine discovered that this puzzle has a solution
for seven pencils too. So, after you solve the challenge with six pencils,
add to them one more pencil, and try to discover that incredible 7-pencil
solution.
What is the minimum number of moves needed to interchange circles with
squares? A piece - either a circle or a square at a time - can be moved on
a vacant adjacent cell to the right, left, up, down or diagonally.
A farmer wants to get his goat, wolf and cabbage to other side of the
river. His boat is only big enough to carry him and either his goat, his
wolf or his cabbage. If he leaves the goat alone with the cabbage, the
goat will eat the cabbage. If he leaves the wolf with the goat, the wolf
will eat the goat. Only when the farmer is present are the goat and the
cabbage safe from their predators. How does he manage to get everything to
the other side?
