# How many people guessed correctly?

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 only one fruit correctly, and 31 people have guessed only two fruits correctly.

1. How many people have guessed three fruits correctly?
2. How many people have guessed four fruits correctly?

• Is there any information about being right or wrong after guessing a the content of 1 box? What prevents someone (who doesn't care about guessing them all correct) from guessing the same fruit at different boxes? Commented May 28, 2018 at 14:23

1. How many people have guessed three fruits correctly?


None.

2. How many people have guessed four fruits correctly?


10 people guessed 4 fruits, because if they guessed 3, they guessed the last too.

• hmmm, you were faster
– Nank
Commented May 28, 2018 at 12:12
• Gotta go fast! :) Commented May 28, 2018 at 12:12
• "How many people have guessed three fruits correctly?" - the question did not ask for how many people have guessed ONLY three fruits correctly. So the answer should also be 10, same as the number of people guessing 4 fruits correctly. Commented May 28, 2018 at 22:22
• So out of 123 people, none of made an impossible guess? Commented May 28, 2018 at 23:04

0 have guessed 3 fruits
10 have guessed 4 fruits

because

You can't guess only 3 fruits because the last one has to be in the last box