Hands On Puzzles Grade 3

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Color the Squares
Color the Squares
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.
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Rep-Tiles
Rep-Tiles
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.
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Counting Polyominoes
Counting Polyominoes
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 Ė 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?
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Circletown
Circletown
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 Patís house, but today Sandy will be driven to Patís house. The map shows where they live. Find a route so that Sandy can visit Pat. The route must start at Sandyís house and end at Patís house, and you have to follow the rules.
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Karate Frog
Karate Frog
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. (Thatís 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 doctorís lilypad is exactly 5 lilypads away. If he hops 11 forward and 7 backward, he just misses the doctorís lilypad. How can Sammo hop to his doctorís lilypad?
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Bookworm
Bookworm
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?
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Six Coins
Six Coins
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?
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Two Match Squares
Two Match Squares
24 matchsticks are used to form the figure in the illustration. Remove 8 matchsticks and end up with just two squares.
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4-Parted Square
4-Parted Square
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?
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The Six Pencils
The Six Pencils
by Henry E. Dudeney
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.
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Circle-Square Interchange
Circle-Square Interchange
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.
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4-to-3 Squares
4-to-3 Squares
Relocate 3 matchsticks to new locations and end up with three squares of the same size. Be sure to use each matchstick as a side of a square.
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The Line-Up Problem
The Line-Up Problem
By moving only one glass of water, line up the glasses so that full ones and empty ones alternate.
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An Old Classic Problem
An Old Classic Problem
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?
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Last Updated: September 10, 2009 top
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