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TAKE AWAY 3 matchsticks to make the equation true.

A Collection

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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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Shown in the puzzle above are one- and two-way roads. In total, how many different routes are there from point A to point J? You may only move in the direction of the matchstick heads and only travel on the same road once during the route.

There are 12 routes in total:

1. ABCFJ

2. ABEFJ

3. ABEHJ

4. ADEBCFJ

5. ADEFJ

6. ADEHJ

7. ADGHEBCFJ

8. ADGHEFJ

9. ADGHJ

10. ABEDGHJ

11. ABCFEDGHJ

12. ABCFEHJ

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5 matchsticks, placed horizontally and vertically, divide the square into 2 equal parts as shown above. The 2 parts are equal in shape and size. Another obvious solution would be 1 vertical and 4 horizontal matchsticks based on the same principle.

But there is another clever solution! In what other way can you place the 5 matchsticks inside the square to divide it exactly into 2 parts equal in shape and size?

AC is exactly the length of 3 matchsticks and BC exactly 4 matchsticks. Applying the Pythagoras's theorem you can proof that AB is exactly the length of 5 matchsticks:

(AB)² = (BC)² + (AC)²

(AB)² = 16 + 9

AB = √25

AB = 5

(AB)² = (BC)² + (AC)²

(AB)² = 16 + 9

AB = √25

AB = 5

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This puzzle is similar to numbers 492 and 502.

14 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 1 matchstick it can be achieved. Which matchstick would you change and can you find the pathway?

The direction of matchstick 3 is changed.

One pathway is to start with matchstick 1 and end with matchstick 14.

One pathway is to start with matchstick 1 and end with matchstick 14.

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