Problem #1
John learned how to count in a base different from 10, so that, for instance, instead of writing 136, he writes 253. In what base does he count?
Problem #2
The product of four consecutive whole numbers is 3024. What are these numbers?
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Solutions from 03/26/2015
Problem #1
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 42 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?
Solution:
Problem #2
A large water tank has two inlet pipes (a large one and a small one) and one outlet pipe. It takes 1 hours to fill the tank with the large inlet pipe. On the other hand, it takes 6 hours to fill the tank with the small inlet pipe. The outlet pipe allows the full tank to be emptied in 7 hours.
What fraction of the tank (initially empty) will be filled in 0.73 hours if all three pipes are in operation?
Solution:
Congratulations to Suhas Pathak, who was the winner of the last set of puzzles.
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