Problema Solution
Amber uses 100 tulips in her flower arrangements. For the vases to look unique, each arrangement should have a different number of tulips, but contain at least 1 tulip. What is the maximum number of arrangements that she can make using exactly 100 tulips?
Answer provided by our tutors
let n = the maximum number of arrangements
we will get maximum number of arrangements if we start with an arrangement containing just 1 tulip and increase the number in each new arrangement by 1 thus for the total number of tulips used we will have
1 + 2 + 3 + .... + n <= 100
n(n+1)/2 <= 100
by solving we find
n <= 13.65
since n is integer follows n = 13 is the maximum number of arrangements.