BrainDen.com - Brain Teasers
• 0

# What’s the least number?

## Question

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

59 were men

72 were football- and baseball-card collectors

81 were college graduates

89 were right-handed

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

## Recommended Posts

• 0

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

59 were men

72 were football- and baseball-card collectors

81 were college graduates

89 were right-handed

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

Am I missing something here? Isn't this simple arithmetic (deduction actually)? It's 31, right? I didn't show my reasoning because for some reason I think I've reasoned incorrectly. That is a reasonable assumption based on reasonable doubt. Come on, let's be reasonable, if for no other reason than ... that's it, it is unreasonable to go on with these puns (i.e. no rhyme nor reason).
##### Share on other sites

• 0
Oops, I just voted this down by mistake. Sorry Trollman. It was a slip of the click.
##### Share on other sites

• 0

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.

So the answer is 1.

##### Share on other sites

• 0

This looks suspiciously like homework...

##### Share on other sites

• 0

well, IQ154, with a name like mine who wouldnt downrate me

Homework?

Are you saying you didnt enjoy this puzzle!?

sditty, good job.

Edited by TrollMan
##### Share on other sites

• 0

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

59 were men

72 were football- and baseball-card collectors

81 were college graduates

89 were right-handed

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

There are 41 women. Assuming all women are part of all groups. The least number of men that satisfy all the criteria is min of ((72-41), (81-41),(89-41)). Which makes it 31 men who were both football- and baseball-car collectors and right-handed college graduates.
##### Share on other sites

• 0

No. of total women = 100 - 59 = 41

If all the 41 women had been football- &amp; baseball-card collectors, then least no. of men who are football &amp; baseball collectors = 72 - 41 = 31.

Similarly least no. of men who are college graduates = 81 - 41 = 40.

------do------------------------------- right handed = 89 - 41 = 48

Then from above it is clear that 31 is the least no. of men who are both football- &amp; baseball- card collectors and righthanded college graduates.

Edited by bhramarraj

• 0

31

Edited by hhh3
##### Share on other sites

• 0

59 men from 100 leaves 41 persons present who are not men (but may be women or children).

Assuming each of the 41 (women or children) were card collectors, college graduates and right-handed, then

72 - 41 = 31 card collectors who were men,

81 - 41 = 40 college graduates were men, and

89 - 41 = 48 men were right-handed.

If 27 men were right-handed college graduates but not card collectors, 20 men were right-handed card collectors but not college graduates, 10 men were card collectors and college graduates but not right-handed, and 1 man who was a college graduate but neither a card collector nor right-handed, then there would be 1 man who was a right-handed card collector and college graduate -- the minimum possible number (given the givens).

##### Share on other sites

• 0

I looked at it backwards. A maximum of 28 men could be non-card collectors, a maximum of 19 men (who could all be different than the 28 non-card collectors) could be non-graduates, and a maximum of 11 men (who could all be different than the 28 non-card men and 19 non-grad men) could be left-handed. 28 + 19 + 11 = 58.

So at least one man must be a right-handed card collecting graduate.

##### Share on other sites

• 0

Would it not be asier to think that the MINIMUM number of right handed college grads, that are dual card collectors, would be 1. This is because the MINIMUM number of people in total can only be one. It easier to think first without using maths.

##### Share on other sites

• 0

Ok, so.

The lease number to have EVERY condition.

So because ALL conditions need to be met, we are adding finding out how many DONT have degrees, are NOT right handed, and DONT collect both and subtracting them from 100.

if 59 are men the minimum number of be men is 59.

Both men and baseball and football card collectors, so: 59 - (100-72) = 31 (the minumum number who are both men and collect BOTH kinds of cards)

Men, collectors of both cards and college graduates: 59 - (100-72) - (100-81*grads*) = 12 (The minumum number of men who are collectors of BOTH cards AND grads)

Men who collect both cards, are grads AND right handed: 59 - (100-72) - (100 - 81) - (100 - 89) = 1

So what I am saying is that

41 people were NOT men

28 people were NOT collectors of both

19 people were NOT graduates

11 people were NOT right handed

And they are not all the same people so

41 + 28 + 19 + 11 = 99 (the possible number of people who dont meet ALL the conditions)

Therefor 100 - 99 = 1 (only one person must be all 4 of those conditions), Though most of them fulfil 3 of the 4 criteria in this scenario.

Statisitacically the avererage answer is 30.62 people fulfilled all of those conditions on the day, but as we know, statistics is the science of guessing so for sure its possible it could have been 59 of them (the lowest single condition needed).

If the question was OR not and, it becomes a whole lot harder...

##### Share on other sites

• 0

if all the women were collectors of both kinds of cards, then there would only be 31 men who were collectors of both types of cards

if all the women were right handed, there would be 48 right handed men

if all the women were college graduates, there would be 40 college graduate men

within the 48 men that were right handed, there would only have to be 20 who were collectors of both types and 29 who were college graduates if the 11 left handed men met those two conditions

due to the fact that 20 + 29 is only 49, only one man has to meet all three conditions for the statistics to be satisfied

Therefore, the answer is 1

##### Share on other sites

• 0

The best way to do this is to take the Negative of the stated conditions:

Not Men = 100-59 = 41

Not FBCC = 100-72 = 28

Not CG = 100-81 = 19

Not RH = 100-89 = 11

So, a total of 99 people might NOT be have one or more of the above characteristics.

Which leaves us with a MINIMUM number of 1 person who will definitely have the above characteristics.

##### Share on other sites

• 0

<p>There is 59 men, out of a 100 people would leave 41 woman. For each&nbsp;scenario the amount of woman has to be subtracted to give the least amount of men in each scenario the results being 31 least amount of men for card collectors, 40 least amount of men for college grads, 48 least amount of men right handed. The question ask for the least amount of men between the 2&nbsp;categories&nbsp;of football and baseball car collectors and right handed men, which is comparing the results of 31 and 48. One might concluded that 31 one is the least amount, but 31 only works for the collectors not the right handed category, so 48 is answer.</p>

##### Share on other sites

• 0

Wow, I can't believe the number of wrong answers on here

##### Share on other sites

• 0

Yes, that shows that it's a good puzzle--it was clearly stated, but still people got different answers. A lot of us learned something here.

##### Share on other sites

• 0

There were 59 men,

Let us assume there were 28 men who were not sports card collectors, leaving 31 men

Of the remaining men, 19 were not college graduates, leaving just 12 men

11 of the remaining men happened to be left handed, leaving a minimum of 1 man who met none of the other criteria

##### Share on other sites

• 0

Not men = 100 - 59 = 41

Least no of men who are card collectors = 72 - 41 = 31

Out of these 31 men, there may be (100 - 81 = 19) non-college grads;

thus least no of men who are card collectors and college grads = 31 - 19 = 12

Out of these 12 men, there may be (100 - 89 = 11) who are left-handed;

thus least no of men who are card collectors and college grads and are right-handed = 12 - 11 = 1

Edited by Sheila Chong
##### Share on other sites

• 0

59 men, 41 women

72 are card collectors. Worst case, assume all 41 women are card collectors. So, 31 men are card collectors and 28 are not.

81 are college graduates. Worst case, all women and non-card collectors are college graduates. So, 41+28=69 graduates are either women or dont collect cards. Remaining 12 (81-69) are graduate men who collect cards.

89 are right handed. Worst case, consider remaining 88 (100-12) are right handed. So, only one out of 12 is a graduate man who collects cards and is right handed.

Answer: At least 1.

Is this correct?

##### Share on other sites

• 0

Wow, guess when you get old the brain doesn't work so well.....this is my first try at this so, maybe in about 50 more I might get it.

##### Share on other sites

• 0

^ slow and steady wins the race =)

59 men, 41 women

72 are card collectors. Worst case, assume all 41 women are card collectors. So, 31 men are card collectors and 28 are not.

81 are college graduates. Worst case, all women and non-card collectors are college graduates. So, 41+28=69 graduates are either women or dont collect cards. Remaining 12 (81-69) are graduate men who collect cards.

89 are right handed. Worst case, consider remaining 88 (100-12) are right handed. So, only one out of 12 is a graduate man who collects cards and is right handed.

Answer: At least 1.

Is this correct?

Yes, you got it!

Edited by TrollMan

## Join the conversation

You can post now and register later. If you have an account, sign in now to post with your account.

×   Pasted as rich text.   Paste as plain text instead

Only 75 emoji are allowed.

×   Your previous content has been restored.   Clear editor

×   You cannot paste images directly. Upload or insert images from URL.