# Honus Bonus

There were 100 people present at a baseball-card show:

59 were men
72 were football/baseball-card collectors
89 were right-handed

What is the least number of men who were both football/baseball-card collectors and right-handed college graduates?

### 2 guesses to Honus Bonus

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• anant

There are 41 women, 28 persons who do not collect any card, 19 persons who are not college graduates and 11 left handed persons. Even if they do not overlap, they add up to only 99. Therefore, there is at least one person who is a right handed man, who is a college graduate and who collect football/baseball-cards

• Dude

Anant, you nailed it.

There are 41 women. (100-59)

If all the women were dual card collectors, that means minimally 31 men are such collectors. (72-41)
If all women are college grads, then minimally 40 men are college grads. (81-41)

If all women are right handed, then minimally 48 men are right handed. (89-41)
If all left handed men are college grads, then minimally 29 men are right handed college grads. (40-(59-48))

So we have 31 men who are dual card collectors and 29 men who are right handed college grads. The minimum overlap of these two sets within a total of 59 men is 1.