You have one hundred marbles, and an infinite supply of trash bags. If you were to put the marbles in the bags, so that no two bags had the same amount of marbles, what is the most bags that you could use?
IŽll use this srategy:
The 1st bag has 1 marble
The 2nd bag has 2
The 3rd bag has 3......
until all 100 have been used.
so we have an equation
100=1+2+3+4..+n
It has been proved that sum 1+2+3..+n equals
n(n+1)
-------
2
->
n(n+1)
100= ------- /*2
2
200=n(n+1)
and then we have a quadratick equation:
n²+n-200=0
where a=1
b=1
and c=-200
-1±√1²-4*1*(-200)
n=--------------------------------
2*1
=-1±√801
--------------------
2
n=27 or n=-2 (not right)
Answer=27 bags
Sum
