Hands On Puzzles Grade 6

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The T Puzzle
The T Puzzle
This puzzle dates back to the beginning of the 20th century, and since then it was many times produced as an advertising puzzle. The goal is to make of these four pieces a symmetric capital T. You're allowed to rotate the pieces as you wish and even turn them over, but they must not overlap each other in the final letter. In fact there are two symmetric capital T letters that you can get from these pieces. Try to find both of them. By the way, there is at least one more extra symmetric shape that can be formed from this set - isosceles trapezoid. Can you find it too?
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The Quarrelsome Neighbors
The Quarrelsome Neighbors
by Sam Loyd
Three neighbors - the owners of the skyscraper, the bungalow and the cottage - who share the small park, as shown in the illustration, have a falling out. This led them to the decision to build three pathways from their houses to the gates of the park (every path to another gate), so that none of the paths cross each other! The owner of the skyscraper wants to build the path to the central gate. The owner of the bungalow (on the left) wants to make the path to the gate on the right, and the owner of the cottage (on the right) wants to have his path to the left gate. The colors of the lawns around the houses and the respective spots next to the gates will help you to understand their plan. Please, notice that none of the path can go behind the skyscraper (see the Top view). How do the quarrelsome neighbors have to build their pathways?
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Seven by 3
Seven by 3
Divide the image of apples above with three lines into seven sections each containing exactly one apple.
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No More Squares
No More Squares
by Martin Gardner
Arrange the 4x4 match square grid as shown in the illustration. The object of the puzzle is to remove nine matches so that no square (of any size) will remain.
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TLs
TLs
by Sam Loyd
Rearrange the eight pieces (one T-shape and seven L-shapes) so that to form the 8x8 checkerboard shown in the center of the illustration.
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The Knight's Tour
The Knight's Tour
by Martin Gardner
Draw the chess board shown in the topmost illustration or just print it out. Place a chess knight (or a simple coin) in any cell of this board. The object is to visit with the knight every cell of the board exactly once, and return to the initial cell where your trip began from. Two bottom diagrams, a and b, show some possible moves of the chess knight which always moves either one cell in one direction, and then two cells in another direction, or vice versa.
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Four into One
Four into One
The four identical equilateral triangles can be arranged together to make exactly the same equilateral triangle, only bigger, just as shown in the upper left illustration. The object is to arrange the four shapes shown in the center of the illustration into the same shape as one of those shapes is, only bigger. You are allowed to rotate and flip the shapes as you wish but the pieces are not allowed to overlap in the final shape.
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Nine Points
Nine Points
Connect all the nine points above with exactly 4 connected straight lines without lifting your pencil off the paper.
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Cube Nets
Cube Nets
A cube has six faces but does every net made up of six squares fold into a cube? Just by looking at the seven patterns here, can you tell which ones can be folded into a perfect cube box?
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Mobius Strip
Mobius Strip
Bizarre shapes and strange connections make math interesting and nothing is more strangely fascinating than the simplicity and topology of the Mobius strip. The nineteenth-century German mathematician A. F. Mobius discovered that it was possible to make a surface that has only one side and one edge. Although such an object seems impossible to imagine, making a Mobius strip is very simple: take a strip of ordinary paper and give one end a twist, then glue the two ends together. And there it is. If you begin drawing a line lengthwise down the strip, after one full revolution you will be at the point where you started but on the opposite side of the strip! Drawing the line through another full revolution will find you back at the beginning. Mobius strips are fun to play with, but industrial engineers have made good use of the shape as well. Conveyor belts are often designed as Mobius strips so that the surface wears out half as fast..
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Conditional Quadrilateral
Conditional Quadrilateral
Four sets of strips are shown. Which set of strip cannot be joined to form a quadrilateral?
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The Bracelet Challenge
The Bracelet Challenges
Janet wants to join the three parts above into a bracelet. The jeweler says he has to charge $2 for each link he must cut and resolder. He figures it will cost $6. She figures out a way it will cost $4. How does Janet solve the problem?
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Strips Square Puzzle
Strips Square Puzzle
by Sam Loyd
The short strips are half the size of the long ones. Arrange the eight strips on a plane so that they form three congruent parts.
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Three Square Lots
Three Square Lots
A father has three square lots for his four children. He wants to give each child a piece of land to plant vegetables. How can he divide these lots so each child gets a plot the same size and shape?
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