The train in the upper illustration must turn around and head back to
Edmonton. After turning, the train and the railway car should be facing
towards Edmonton as shown in the lower illustration. The engine and the
railway car can be coupled and uncoupled in any way. The engine can push
and pull with its front end as well as its back end. There is just enough
room for one car or engine on the straight part of the sliding, and enough
room for both the engine and the car at the other straight part of the
track past the sliding. While the car and engine are being moved to their
new positions, they can face different directions.

The train in the upper illustration must turn around and head back to
Edmonton. After turning, the train and the railway car should be facing
towards Edmonton as shown in the lower illustration. The engine and the
railway car can be coupled and uncoupled in any way. The engine can push
and pull with its front end as well as its back end. There is just enough
room for one car or engine on the straight part of the sliding, and enough
room for both the engine and the car at the other straight part of the
track past the sliding. While the car and engine are being moved to their
new positions, they can face different directions.

A certain country uses gold coins called buckazoids. The coins weigh the
same as their denominations. A 1-buckazoid coin weigh 1 gram, a
2-buckazoid coin weighs 2 grams and so on. Problem 1. Someone has given
you two 1-buckazoid coins, one 2-bucazoid coin, and one 3-buckazoid coin.
One of them is fake; it weighs too much. How can you find the fake coin by
using only a pan balance? You have no other weighs except for these four
coins. Problem 2. How would you find the fake coin if all you knew was the
wrong weight but didn’t know whether it was too heavy or too light?

This is the same problem as
Buckazoid Arithmetic – Basics except that
someone has given you one 1-buckazoid coin, two 2-bucazoid coin, and one
3-buckazoid coin. One of them is fake – it doesn’t weigh what it should –
but you don’t know whether it is heavier or lighter than a real coin. How
can you find the fake coin by using only a pan balance? You have no other
weights except for these four coins.

This is the same problem as
Buckazoid Arithmetic II except that the four
coins are one 1-buckazoid coin, one 2-buckazoid coin, one 3-buckazoid
coin, and one 5-buckazoid coin. Once again, of them is fake – it doesn’t
weigh what it should – but you don’t know whether it is heavier or lighter
than a real coin. How can you find the fake coin by using only a pan
balance? You have no other weights except for these four coins.

You are a pilot of a spaceship. You have to travel home from a star base.
The only way is to take the space tunnels that connect through three space
stations. However, it takes a lot of fuel to travel through a space
tunnel. For each space tunnel it takes one energy couple. You have 6
energy capsules at the star base, but your spaceship can only carry 3 at a
time and you will have to pass through 4 space tunnels. You can store
energy capsules at the space stations.

This is like
Easy Space Travel. To get home, you will have to pass through
11 space stations and twelve space tunnels. For each space tunnel it takes
one energy capsule. You have 24 energy capsules at the star base, and your
spaceship can carry up to 8 at time. You can store energy capsules at the
space stations.

Two trains, one of an engine and a car and another - of an engine and two
cars, meet at a segment of railroad. There is a switch or side-track on
that segment of railroad - just as shown in the illustration. The switch
is large enough only to hold one engine or one car at a time. The object
is, using only this switch, to exchange the trains in order they can
continue their journeys and do that in the most expeditious way. No other
outside help, except the switch itself, is allowed. Please, note that a
car cannot be connected to the front of an engine.

Can the frog catch the fly? To catch the fly, the frog has to land on the
same lilypad as the fly. The frog and fly can hop from one lilypad to
another that is connected to it by a line. The frog always starts on the
big lilypad at the bottom. The frog has to move first. After the frog
moves, the fly will move, and they continue to alternate moves.

Three boxes contain blue and orange balls. One
box contains 2 blue balls, another one contains 2 orange balls, and a
third one contains 1 blue and 1 orange ball. The boxes have been labeled,
but each of the labels is on a wrong box. All three boxes have lids, and
you cannot see what is in them. However, you are allowed to reach into any
of the boxes without peeking and take one or two balls out and look at
them. Taking out as few balls as possible, figure out what the correct
labels should be.

This is a game for two people. Start by arranging four or more counters in
a circle as shown in the illustration. Players take turns removing one or
two counters. If a player takes two counters, they must be next to each
other with no other counters or open spaces between them. The last player
to take counter is the winner. In this game there is a sure way for the
second player to win.

This is a game for two people. Start by placing 9 counters in three rows
as shown in the illustration. Players take turns removing any number of
counters provided they are all in the same row. The player who is forced
to pick up the last counter loses. There is a sure way for the first
player to win. If the first player doesn’t make the correct move, the
second player can win. This is the classic game of Nim. It can be played
with any number of counters and any number of rows.

Arrange five coins (three bigger and two smaller
ones) as shown above (top row) - Start Position. The problem is to
change their positions to those shown at the bottom of the
illustration (Finish Position) in the shortest possible number of
moves. A move consists of placing the tips of the first and second
fingers on any two touching coins, always of the different sizes, then
sliding the pair to another spot along the imaginary line shown in the
illustration. The two coins in the pair must touch at all times. The
coin at left in the pair must remain at left; the coin at right must
remain at right. Gaps in the chain are allowed at the end of any move
except the final one. After the last move the coins need not
necessarily be at the same spot on the imaginary line that they
occupied at the start.

Sandy’s grandmother lives in an old one-storey house. There are many
connecting doors between the rooms. One day, Sandy wanted to find a route
that would take her through each door exactly ones. Help Sandy find a
route. The illustration shows three different houses’ plans as three
separate challenges.

This is a game for two people. Place 45 counters in a 5 by 9 rectangular
array as shown in the illustration. Players take turns removing counters
according to the following rule. A player divides the counters into two
rectangles by drawing a horizontal or vertical line, and the player must
take all the counters in one of the two rectangles. The one who is forced
to take the last counter is the loser.

Copy and cut out the two identical tangram sets as those shown in the
illustration. Can you combine all fourteen pieces to form one large
square? You can rotate the pieces and turn them over, but it is not
allowed to overlap them.

Can you place the numbers 1 to 12 (except for 7 and 11) on the circles so
that the sum of the numbers on any straight line equals 24? The numbers 3,
6 and 9 have been placed to guide you.

Four sets of strips of different lengths are
shown. The sets are of lengths 1, 2 and 4; 2, 3 and 4; 2, 4 and 5 and
2, 3 and 5. Are there any sets of strips that cannot form a triangle
when joined together?

At first glance this structure seems impossible to build. After all it
would collapse before many of the bricks (or in this case, dominoes) were
laid. But the bridge is actually easy to construct if you approach it with
the right frame of mind.

There are twenty-two gloves in a drawer: five pairs of blue gloves, four
pairs of orange and two pairs of green. If the lights are out and you must
select the gloves in the dark, how many must you choose to ensure that you
have at least one matching pair?