Hi there,
G = green beans
C = Cauliflower
B = broccoli
G + C = 55
C + B = 54
G + B = 56
G + B + C = 53
If 53 students ate all three, then 2 students ate just green beans and cauliflower (55-53)
If 53 students are all three, then 1 students ate just cauliflower and broccoli (54-53)
If 53 students are all three, then 3 students ate just green beans and broccoli (56-53)
So we have
53 eat G, B, C
2 eat G, C
1 eats C, B
3 eat G, B
---
59 students
Now, 59 students eat green beans, then 59-53-2-3= 1 eats green beans only
56 students eat cauliflower, then 56-53-2-1=0 no students eat just cauliflower
60 students eat broccoli, then 60-53-1-3 = 3 eat just broccoli
So now we have
53 eat G, B, C
2 eat G, C
1 eats C, B
3 eat G, B
1 eats G only
0 eat C only
3 eat B only
-----
63 students
But we have 64 students. So one student doesn't eat any of the three vegetables.
3 students eat green beans but not cauliflower
3 students do not eat broccoli (2 +1)
0 students eat only cauliflower
4 students eat exactly two of the three vegetables.
