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.
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
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?
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 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.