# 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? – PL457 May 28 '18 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 May 28 '18 at 12:12
• Gotta go fast! :) – Saeïdryl May 28 '18 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. – Bayequentist May 28 '18 at 22:22
• So out of 123 people, none of made an impossible guess? – Acccumulation May 28 '18 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