In a contest, four fruits (an apple, a banana, an orange, and a pear) have been placed in four closed boxes (one fruit per box). People may guess which fruit is in which box. 123 people participate in the contest. When the boxes are opened, it turns out that 43 people have guessed none of the fruits correctly, 39 people have guessed one fruit correctly, and 31 people have guessed two fruits correctly. The Question: How many people have guessed three fruits correctly, and how many people have guessed four fruits correctly?
It is not possible to guess only three fruits correctly: the fourth fruit is then correct too! So nobody has guessed three fruits correctly and 123-43-39-31 = 10 people have guessed four fruits correctly.
Adored by few, Feared and hated by many. Mistress of the entire universal reason, Master in the art of numbers. Some may have solved many of your mysteries, But there still much of them to find. What are they?
A woman went into a bank to cash an insurance refund check. By mistake the teller gave her dollars for cents and cents for dollars. She put the money in her purse but accidentally dropped a nickel on the floor. When she got home, she found that she had exactly twice the amount of the check she had cashed. She didn't have any money in her wallet before going to the bank. What was the exact amount of that check?
The amount must have been $31.63. She received $63.31. After she dropped a nickel there would remain the sum of $63.26, which is twice the amount of the check.