MathDB

On day

1

of the new year, John Adams and Samuel Adams each drink one gallon of tea. For each positive integer

n

, on the

n

th day of the year, John drinks

n

gallons of tea and Samuel drinks

n^2

gallons of tea. After how many days does the combined tea intake of John and Samuel that year first exceed

900

gallons?
Proposed by Aidan Duncan
Solution.

\boxed{13}

The total amount that John and Samuel have drank by day

n

\dfrac{n(n+1)(2n+1)}{6}+\dfrac{n(n+1)}{2}=\dfrac{n(n+1)(n+2)}{3}.

Now, note that ourdesired number of days should be a bit below

\sqrt[3]{2700}

. Testing a few values gives

\boxed{13}

as our answer.

Problem Statement