121. Create 3 square units with 12 sticks.

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Assume the length of one matchstick is 1 unit.

In figure 1 we used 12 sticks to form an area of 5 square units. In figure 2 we also used 12 sticks, but this time the area is 9 square units.

How would you create an area of 3 square units using 12 sticks and not breaking any of the sticks? This one is not so easy...!

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The total area of the triangle ABC:
= 1/2 X BC X AB
= 1/2 X 3 X 4
= 6 square units

The area marked "D" can easily be calculated as 3 square units.

Therefore the area marked "E":
= Area ABC - Area D
= 6 - 3
= 3 square units

Any other ideas?

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120. Numeric Puzzle : 3X3=5 : Move 1

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Move only 1 stick to make the equation true.

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119. Treasure Rooms and Treasures

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The challenge in this puzzle is to start at the START in Figure 1, to enter each treasure room and to pick up all the treasures (broken sticks) until you get to the END. You may only ENTER and EXIT a treasure room ONCE.

Figure 2 shows the rooms in more detail.

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118. Roman numerals : 4 - 2 is not 5 : Move 1

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The Roman numerals equation shows 4-2=5, which is obviously not true. Move 1 stick to make the equation true.

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117. The King and his Guards: Remove 2 Guards

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A King is protected by 12 guards in his castle as indicated. There are 4 guards needed for each of the 4 walls of his castle. The guards on the corners protect 2 walls.

The King then decides to take 2 guards off duty and to move the remaining guards around so that the security is even better with 5 guards per wall. What did he do?

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116. Add 17 sticks to form 7 Squares.

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Shown here are 2 squares equal in size. One matchstick forms a "shared" side of the 2 squares, hence only 7 sticks are used. Can you add 17 matchsticks to form 7 equal squares by using this principle of "sharing" sticks?

(Try to figure out beforehand how the sticks should be placed as there is some maths involved)

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Above is only one solution, there are also other solutions.

(1) There are 24 sticks in total. (17 + 7 = 24)
(2) 7 squares with no "shared" sides would have required 28 sticks. (7 X 4 = 28)
(3) So there must be 4 squares with "shared" sides. (28 - 24 = 4)

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115. 3X3 Triangle. Remove 5 sticks leaving 4 Triangles.

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Remove 5 sticks leaving 4 triangles. The triangles don't have to be equal in size.

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114. Forming 5 groups with 3 matchsticks in each group.

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Shown here is one row with 15 matchsticks. The challenge is to create 5 groups with 3 sticks in each group. A group is formed by placing the 3 sticks vertically above each other by jumping over 3 other sticks.

For example: Take stick 4, jump to the right over 5, 6 and 7 and place it vertically above stick 8. Now take stick 12 and jump to the left over 11, 10 and 9 and also place it above stick 8. (above stick 4 you just moved) One group of 3 sticks has now been formed. Continue to form 4 more groups. Remember the following:
(1) You can jump to the left or right.
(2) Always jump over 3 sticks.
(3) Sticks already placed must also be counted when jumping.

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There are many solutions, but one solution would be to do the following in sequence:
5 above 1
6 above 1
9 above 3
10 above 3
8 above 14
7 above 14
4 above 2
11 above 2
13 above 15
12 above 15

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113. The Farmer, Four Sons, Diamonds and Gold

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A farmer discovers diamonds and gold on his farm. He decides to live on the area marked "A", exactly in the middle of the farm, and to leave the mining activities to his four sons. Add 12 sticks to show how he should divide the rest of the farm equally between his four sons so that:

(1) all 4 farms have the same shape
(2) there is 1 diamond mine on each farm
(3) there is 1 gold mine on each farm?

Can you solve the puzzle by adding 12 sticks to the existing farm?

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112. Remove 8 leaving 6 squares

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Remove 8 matchsticks leaving 6 squares. The squares don't have to be equal in size.

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111. Ten and Eleven

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Move 1 stick to make the equation true. (Please note these numbers are NOT Roman literals)

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110. 1X1 Square : Add 16 creating 5 equal Squares

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Add 16 matchsticks creating 5 squares equal in size

(If you do some maths beforehand you can actually figure out ho to place them.)

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Forming 5 squares with 20 sticks (16 + 4) means 4 sticks are used per square. (20 / 5 = 4) Therefore, no two squares are adjacent using a common stick to form a side. Understanding this makes the puzzle easy.

There are also other solutions.

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109. 3X3 Square : Remove 8 leaving 2 Squares

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Remove 8 sticks leaving only 2 squares NOT equal in size.

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108. The Numbers 1 to 8 in Squares

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Take 4 matchsticks and break each stick into 5 small pieces. Each broken stick represents a numerical value as shown in Step 1.

Step 2 is just an example and only shows how the numerical values 1 to 8 are represented using the broken sticks.

Now build the layout as shown in Step 3. The challenge is to place the numbers 1 to 8 (using the broken sticks) into the 8 squares so that no two consecutive numbers touch either vertically, horizontally, or diagonally.

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