# 100 each

Number Theory Level 5

A Rich Man once decided to hold a party at his place. He invited 100 guests and arranged for 100 plates of food. The guests were of three social groups: A, B and C.
The members of group A said that they will eat 2 plates each,
The members of group B said that they will eat 4 plates each.
Seeing that the rich man was getting worried, the members of Group C volunteered to eat 4 persons to a plate, thereby solving the man's problem.

Now, no plates were left and all the guests had eaten food.
How many members of each group were there?

Enter the answer as $$0$$ if you think no answer is possible.
Enter the answer as $$a*b*c$$ if there is a unique answer.
Enter the answer as the difference between the highest and lowest values of $$a*b*c$$ if there are more than $$1$$ answers.

Details and assumptions:

• There is at least 1 member of each group.

• Each plate in case of group C must be used by exactly 4 members i.e. you cannot have only 2 members eating from the last plate.

• $$a,b,c$$ refer to number of members of A,B and C present at the party.

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