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

A Collection

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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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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?

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...

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.

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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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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This puzzle is similar to but different from Number 492.

7 matchsticks are used to form a pathway as shown above. The challenge is to start at a point, move in the direction of the matchstick heads and visit each of the 7 matchsticks only once.

A solution is not possible in the existing figure above, but by changing the direction of only 2 matchsticks it can be achieved. How would you do this?

Change the directions of matchsticks 1 and 5. The pathway is then from matchstick 1 to 7.

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