Question

There Are 100 People In A Room. The First Person Gets 1% Of A Pie , And The Second Person Gets 2% Of The Remaining Pie And So On. Who Will Get The Largest Share Of Pie?

Answer 1

Dear student

Let after k−1 guests have had a slice there is X_k-1cake left.

The kth guest gets X_k-1*k/100 cake.

The (k+1)th guest gets X_k-1(1−k/100)*k+1/100 cake.

Let us assume that the (k+1)th guest gets more cake than the kth guest, i.e.:

(1−k/100)k+1/100>k/100

(100−k)(k+1)>100k

−k2−k+100>0

The above equation is true for k=1…9, and it fails for for k≥10, so the 11th guest gets less than the 110th guest, who gets more than the 9th which implies that 10th guest gets the largest share of cake.
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