In a school function ceremony, seven students, Amy, Bob, Chad, Dom, Elisa, Fischer, and Grant have to deliver their performances in seven consecutive slots, not necessarily in the order of their given names. The following information is known about the order in which the students perform:
Chad performs immediately before Dom
Grant performs sometime after Chad
There are exactly two performances made between the performances of Amy and Elisa
What is the maximum number of performers between Fischer and Grant?
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1
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2
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3
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4
thus, the best choice for G is the 7th slot.
We now need to check the earliest possible slot for -
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5
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We can observe that F is a floating element as there is no conditions set on
Thus, F can easily take the 1st slot.
One of the possible orders is shown below:
Thus, there can be a maximum of five performers between F and G.
GeneralLet us denote the seven slots using the numbers 1 through 7 as shown below:

We need to fill in the names of the performers in each slot depending on the information provided.
Let us name the performers Amy, Bob, Chad, Dom, Elisa, Fischer, and Grant as A, B, C, D, E, F and G.
Let us look at the information given in the question stem and see what we have got:
1. Since Chad performs immediately before Dom, we can write "CD" as an element implying that there is no one else performing between them.
2. Since Grant performs sometime after Chad, and Chad and Dom are consecutive performers, Grant must perform after Dom as well. Thus, we can represent theinformation as shown below:
The "…" above implies that there could be none or at least 1 performer between D and G.
3. There are exactly two performers between Amy and Elisa. This information can be represented as shown below:
Thus, we see that the above information is NOT sufficient to assign even one of the performers to his/her corresponding slot number. This implies that there would possibly be multiple solutions to the arrangements of the performers. Thus, in order to solve the questions, we would need to use the information given in the questions.





