Published Wednesday, March 2, 2011 by Tarang

Get your math brains going on these logic problems. Have fun! Leave your answers to the questions as comments:

1. You have a 3 gallon jug and a 5 gallon jug. You need to measure out exactly 4 gallons of water. How do you do it?

2. You have 4 stones of exact color, size, etc. except one of the stones is either heavier or lighter than the other 3. You are given a balance. How do you figure out which stone doesn’t belong in just two measurements of the balance?

3. A rich merchant had collected many gold coins. He did not want anybody to know about them. One day, his wife asked, “How many gold coins do we have?”
After pausing a moment, he replied, “Well! If I divide the coins into two unequal numbers, then 32 times the difference between the two numbers equals the difference between the squares of the two numbers.”
The wife looked puzzled. Can you help the merchant’s wife by finding out how many gold coins they have?

4. You have 100 balls divided evenly into ten boxes (ten balls in each box). One of the boxes contains balls that are 1.5 grams lighter than the balls in the other boxes. You are given a weigh balance. How do you figure out which of the ten boxes contains the balls that are 1.5 grams less by using the balance. (Note: The boxes are numbered 1 through 10 and so are the balls from the boxes i.e. a ball from box 2 will be labeled 2)

5. In a far away land, it was known that if you drank poison, the only way to save yourself is to drink a stronger poison, which neutralizes the weaker poison. The king that ruled the land wanted to make sure that he possessed the strongest poison in the kingdom, in order to ensure his survival, in any situation. So the king called the kingdom’s pharmacist and the kingdom’s treasurer, he gave each a week to make the strongest poison. Then, each would drink the other one’s poison, then his own, and the one that will survive, will be the one that had the stronger poison.
The pharmacist went straight to work, but the treasurer knew he had no chance, for the pharmacist was much more experienced in this field, so instead, he made up a plan to survive and make sure the pharmacist dies. On the last day the pharmacist suddenly realized that the treasurer would know he had no chance, so he must have a plan. After a little thought, the pharmacist realized what the treasurer’s plan must be, and he concocted a counter plan, to make sure he survives and the treasurer dies. When the time came, the king summoned both of them. They drank the poisons as planned, and the treasurer died, the pharmacist survived, and the king didn’t get what he wanted.
What exactly happened there?

6. I have three friends. Two play football, two play tennis and two play golf. The one who does not play golf does not play tennis, and the one who does not play tennis does not play football. Which games does each friend play?

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