590. Balance the scale: Move 1

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The vertical matchsticks on the scale all have the same weight. To balance the unbalanced scale you need to MOVE 1 matchstick. Where would you place it?

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In the original puzzle:

Left of balancing point: (3x1) + (1x1) + (1x1) + (1x1) = 6 units
Right of balancing point: (3x1) + (4x1) = 7 units

From the above we can see we need to move a matchstick right of the balancing point. This is done by placing the matchstick as shown in the solution.

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589. Missing number

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This puzzle is extremely difficult because you would have to think out of the box to solve it!

Replace the "?" with the missing number in the sequence.

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First you need to turn the figure by an angle of 180 degrees. Then replace the "?" with "87" to form a sequence 86, 87, 88 and 89.

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588. Route Map: Change one direction

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13 matchsticks are used to form a pathway as shown above. The challenge is to start at point A, move in the direction of the matchstick heads, visit each of the 13 matchsticks only once and finish at point B.

A solution is not possible in the existing figure above, but by changing the direction of only 1 matchstick it can be achieved. How would you do this?

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Change the direction of matchstick 10. The pathway is then from matchstick 1 to 13.

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587. Mathematical: 0 minus 5 is not 1

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MOVE only 1 matchstick to make the statement true.

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586. Little square and rectangle

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Four matchsticks form a little square as shown above. Your challenge is to create a rectangle with size EXACTLY 3 times the size of the little square.

Note the following:
1. All matchstick heads have been removed.
2. The 4 matchsticks are exactly the same. (thickness, length etc)
3. Only the 4 matchsticks above may be used in your solution.
4. Not all matchsticks have to be used in your solution.
5. You are allowed to break one matchstick.

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585. Four-sided figures

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A four-sided figure (square or rectangle) can be stand-alone or combined. How many four-sided figures do you count with at least one broken matchstick in them?

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There are 14 four-sided figures in total

Stand-alone: C, D, G
Two combined: B+C, D+E, D+F, F+G, G+H
Three combined: A+B+C, F+G+H, E+G+H
Five combined: A+B+C+D+E, D+E+F+G+H
Eight combined: A+B+C+D+E+F+G+H

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584. The four rectangles

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There are 3 rectangles of size 2X1 in the layout above. They are ABDC, EGLJ and FHMK.

Move 3 matchsticks to create FOUR equal rectangles each of size 2X1.

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The four 2X1 rectangles are ABDC, FHMK, CDON and GPQL

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583. Divide the square

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Divide the square into 3 parts by adding 8 matchsticks. The 3 parts must be equal in size but not necessarily in shape.

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582. Mathematical: 4 plus 5 is not 5

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MOVE 3 matchsticks to make the equation true. Consider yourself brilliant if you can find the 3 solutions.

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581. Remove 6 leaving 3 squares

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Take away 6 matchsticks to leave you with 3 equal squares. The 3 squares may not touch.

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580. Divide the rectangle in ratio 3:4:5

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Divide the rectangle into 3 areas with ratio 3:4:5 by placing 7 matchsticks inside the layout.

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There are also other solutions.

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579. Mathematical: 6 plus 0 is not 7

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TAKE AWAY 4 matchsticks to make the equation true.

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578. Remove 3 leaving 3 triangles

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TAKE AWAY 3 matchsticks to leave you with 3 equal triangles.

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577. One square

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Place the 8 matchsticks in such a way that it forms a square. The 4 broken matchsticks have the same length but are not half the length of the full matchstick.

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576. Divide into 4 areas

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Add 15 matchsticks inside the layout above to create 4 areas equal in SIZE.

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575. Three matchstick node notations

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Figures A and B above are two examples illustrating how "nodes" and "node notations" are formed by using 3 matchsticks. There are 7 more "node notations" using only 3 matchsticks. Can you find them all?

The rules are:
1. Matchstick heads can be ignored
2. All matchsticks must be flat on the surface
3. Each matchstick must touch at least one other matchstick

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574. Triangle 3X3: Remove 4 leaving 6 triangles

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Take away 4 matchsticks to leave only 6 triangles. The triangles must be equal in size.

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There are also other solutions.

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573. The third grader puzzle

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This puzzle was given to third graders in a school somewhere in the world...

ADD only 1 matchstick to make the equation true.

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572. Mathematical: 4 minus 7 is not 8

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TAKE AWAY 3 matchsticks to make the equation true.

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571. Change the 2:3:4 ratio to 1:1:1

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The above square is divided into 3 parts in the ratio 2:3:4. The ratio must be changed to 1:1:1 by moving only 1 matchstick.

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The ratio 3:3:3 is equal to 1:1:1.

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570. The biggest number

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ADD 3 matchsticks to form the BIGGEST possible number. Your solution should only have THREE digits.

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569. Divide into 4 areas

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Add 10 matchsticks inside the layout above to create 4 areas equal in SIZE and SHAPE.

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568. Change to numerical equation

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The above equation is not true. Move 2 matchsticks to change it to a valid numerical equation.

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567. The wood log problem

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In a factory are 5 machines with each machine producing 5 pieces of compressed wood logs. The weight of each wood log is 500 grams.

However, one of the 5 machines is faulty and produces 5 logs with weight slightly more than 500 grams for each log. You do not know which machine is faulty and also not by how much.

Available in the factory is a digital single-tray scale. (not a two-tray balance scale) You are allowed to weigh as many logs as you wish at a time, but may use the scale only twice. How can you find the faulty machine?

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STEP 1:
Place one log from each machine on the scale and weigh. Let's assume your answer is 2 510 grams. You now know the faulty machine produces 10 grams more for each log. (2 510 grams - 2 500 grams) But you still don't know which machine is faulty...

STEP 2:
Place the logs on the scale as shown above. The total weight is supposed to be 7 500 grams. (15 logs X 500 grams) Let's assume your answer is 7 530 grams which means there are 30 grams more than expected. (7 530 grams - 7 500 grams) Your faulty machine would therefore be machine 3. (30 grams / 10 grams) If machine 1 was faulty the weight would have been 7 510 grams, machine 2 would be 7 520 grams etc.

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566. Matchstick Grid: Diagonal heads

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This puzzle is similar to but different from number 500.

If you count the matchstick heads in each diagonal, vertical and horizontal row you will get to the numbers as shown above.

Your challenge is to rearrange the matchsticks to have:
- 4 heads in each row
- 4 heads in each column
- 8 heads in each diagonal row.

Your solution must still be a 2X2 matchstick grid.

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