[bonanova]

There are 189 members of the tennis club:

8 have been at the club less than three years;

11 are less than 20 years of age;

70 wear glasses;

140 are men.

What is the minimum number of players who had

been members for three years or more,

were at least 20 years of age,

wore glasses and

were men?

[akaslickster]

um 129

[bonanova]

um 129

A tad high.

Nice try tho.

[akaslickster]

126

[Guest]

70?

[Guest]

2

That's what I came up with using this, using lists generated in Excel.

I started with the two smallest lists, got the minimum overlap (21), then for each of the remaining sets took out as many as I could from the overlap, which was always the remainder of the total set.

So, while getting there was a bit hairy, the solution actually turned out to be simple, if only I had known what I was doing from the start: 189-(189-70)-(189-140)-(189-178)-(189-181)

[Guest]

There are 189 members of the tennis club:

8 have been at the club less than three years;

11 are less than 20 years of age;

70 wear glasses;

140 are men.

What is the minimum number of players who had

been members for three years or more,

were at least 20 years of age,

wore glasses and

were men?

I think

2.

I assume following config.

49 women and wear glasses

140 men out of which

21 wear glasses(The only people that qualify)

Out of these 21:

11 are less than 20 years old

So 10 remaining from which 8 have been less than 3 years

So two are left

[bonanova]

Duh Puck and imran have it.

Good job.

Wow Duh Puck - great resource.

I think you've destroyed any future VD [that's in the logical sense] puzzles.

Great find.

[Guest]

I think

2.

I assume following config.

49 women and wear glasses

140 men out of which

21 wear glasses(The only people that qualify)

Out of these 21:

11 are less than 20 years old

So 10 remaining from which 8 have been less than 3 years

So two are left

Wow, I learn my mistake here! Thanks for Imran and your explanation. I try to work the opposite way and it also works!

Assuming all the 119 person who don't wear glasses are all men, so the minimum men who wear glass = 140 (men) - 119 (w/o glass) = 21.

Then the maximum member who younger than 20 yrs old it can be are those men who wear glass, then those men wear glass and at least 20 yrs old left 21-11 = 10 (minimum)

then the maximum memeber who join less than 3 yrs it can be are those men (with glass) and (younger than 20 yo),

so the minimum member who fulfill the cirteria = 10 - 8 = 2 !