A number of guests gather around a round table for a dinner.Between every adjacent pair of guests, there is a plate for tips.When everyone has finished eating, each person places half theirtip in the plate to their left and half in the plate to theirright. Suppose you can only see the amount of tips in each plateafter everyone has left. Can you deduce the amount that eachindividual tipped?

(a) Suppose six guests sit around a table and there are sixplates of tips. If we know the amount of tip in each plate, P1 toP6, can we determine each individual’s tip amount, G1 to G6 (G1+G6= P1, G1+G2 = P2, G2+G3 = P3, ... , G5+G6 = P6)? If yes, explainwhy by examining the relationship between the plate values, P1 toP6, and guest tips, G1 to G6. If not, give two differentassignments of G1 to G6 that will result in the same P1 to P6.

(b) Now lets consider five guests at the table, G1 to G5, and wecan see the amount of tips in the five plates, P1 to P5 ((G1+G5 =P1, G1+G2 = P2, G2+G3 = P3, ... , G4+G5 = P5)). In this new settingcan you figure out each guests tip values, G1 to G5?

(c) If n is the total number of guests sitting around a table,for which values of n can you figure out everyone’s tip? You do nothave to rigorously prove your answer. (Hint: consider what isdifferent about parts a and b.)