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# You're super genius if you solve this Puzzle

## Question

There are 90 students at school, 30 students participate at football team, 40 students participate at Volleyball   team and 25 students participate at Basketball team.

15 students are participating in football team & Volleyball team.

10 Students are participating in football team & Basketball team.

8 Students are participating in Volleyball team & Basketball team.

23 Students not participating at any team, whereas there are students participate at three teams.

How many students participating at three teams?

How many students participating at Football team only?

How many students participating at Volleyball team only?

How many students participating at Basketball team only?

## 13 answers to this question

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Will upload diagram a bit later. Can pretty much fill it out from the description.

Venn diagram

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Edited by Thalia

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In order:

5, 10, 22, 12

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Something is wrong with one or more of the numbers in the OP!

Spoiler

Edited by rocdocmac
Reworded

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5 minutes ago, rocdocmac said:

Something is wrong with one or more of the numbers in the OP!

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When it says a student plays 2 sports, that doesn't mean they don't play the 3rd sport. So I think when you subtract 2X, you're subtracting students already accounted for.

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40 minutes ago, Thalia said:

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When it says a student plays 2 sports, that doesn't mean they don't play the 3rd sport. So I think when you subtract 2X, you're subtracting students already accounted for.

Spoiler

The middle section has been counted three times, one for each group, so we must subtract it twice in order to count it once ultimately. What does the Venn diagram for your solution look like?

Edited by rocdocmac

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5 hours ago, rocdocmac said:

Something is wrong with one or more of the numbers in the OP!

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Excellent try, this formula can be used only EXACTLY number of FV ONLY , EXACTLY number of FB ONLY and EXACTLY number of VB ONLY.

5 hours ago, Thalia said:

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When it says a student plays 2 spo﻿rts, that doesn't mean they don't play the 3rd sport. ﻿So I think when you subtract 2X, you're subtracting students already accounted for.

Yes, that's right.

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5 hours ago, rocdocmac said:

Boo.  Dumb phone. Nothing to see here...

I added up the number of students in each of the sports (30,40,25). That's 95. We know there's 23 students who don't play those sports so 67 remaining. That means there's a 28 student overlap. Adding up the given overlaps (15,10,8) gives you 33. So the overlap for those is 5. I subtracted from the appropriate sections of my diagram as I went.

Edited by Thalia
Phone quoting issues.
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46 minutes ago, Thalia said:
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I added up the number of students in eac﻿h of the sports (30,40,25﻿). That's 95﻿.﻿ We know there's 23﻿ students who don't play those sports s﻿o 67﻿ remaining﻿﻿. Tha﻿t mean﻿s there's a 28 stude﻿﻿nt﻿ o﻿ver﻿lap﻿. Adding up the given ﻿overlaps﻿ ﻿(15,10,8) gives you 33.﻿ So the overlap for those is 5. I subtracted from the appropriate sections of my diagram as I went.﻿﻿

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13 hours ago, Thalia said:

Will upload diagram a bit later. Can pretty much fill it out from the description.

Venn diagram

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You're really super genius

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90  students however there are 95 involvements i.e. ( 30 fb;  40 vb;   25 bb ). That there are 23 who do not participate is NOT crucial to the solution.

A ) 15 fb + vb ;  B)  10 fb + bb ;   C) 8 bb + vb ;;           15 fb+ 10 fb =25 fb combined plus 5 ;   15 vb + 8 vb = 23 vb plus 17 ;  10 bb + 8 bb = 18 bb plus 7                                                                 The plus 5 ; plus 17; plus 7 represents respectively those who play only 1 or all 3 sports . =  29                                                                                                                                            Now 25  +  23  +  18 = 66 involvements;  plus 29 involvements = 95 involvements                                                                                                                                                           Therefore the plus 5 ; plus 17; plus 7 represents respectively those who play only 1 sport  and there were none who played all 3 sports

I yield to Rubaidi's  Venn diagram above  great solution

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@Thalia

Well done!

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This site is filled with intelligent people with different strengths. This one just happens to work well with how my brain is wired. Nice puzzle.

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21,15,17,7

90                                               17+15+7+5=44                  44-23=--21

30    40    25

_--15     15    25    15   10

_--17    8  _--7   _5

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