Hands On Puzzles Grade 5

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Turning Train
Turning Train
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.
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Turning Train II
Turning Train II
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.
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Buckazoid Arithmetic - Basics
Buckazoid Arithmetic - Basics
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?
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Buckazoid Arithmetic II
Buckazoid Arithmetic II
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.
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Buckazoid Arithmetic 1235
Buckazoid Arithmetic 1235
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.
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Easy Space Travel
Easy Space Travel
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.
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Space Travel II
Space Travel II
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.
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Simple Train Exchange
Simple Train Exchange
by Sam Loyd
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.
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The Frog and Fly Game
The Frog and Fly Game
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.
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Boxes and Balloons
Boxes and Balloons
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.
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Circle Nim
Circle Nim
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.
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Classic Nim
Classic Nim
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.
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Collating the Coins
Collating the Coins
by Martin Gardner

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.

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Grandma's House
Grandma's House
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.
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Square Nim
Square Nim
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.
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Double Tangram
Double Tangram
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.
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Lucky Cuts
Lucky Cuts
Can you dissect this horseshoe into six pieces with only two straight cuts?
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Magic Pentagram
Magic Pentagram
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.
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Condition Triangle
Condition Triangle

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?

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Hog-Tied
Hog-Tied
Two hostages are tied together by their wrists, as shown. Can they separate themselves without cutting the rope or untying the knots?
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Impossible Domino Bridge
Impossible Domino Bridge
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.
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Gloves in the Dark
Gloves in the Dark
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?
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Middle of the Stick
Middle of the Stick
Using the 8 cm and the 3 cm stick, figure out a way to find the middle of the 8 cm stick.
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Lines of Discs
Lines of Discs

Move just one disc to a new location and end up with two lines of four discs each.

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Last Updated: September 10, 2009 top
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