Enlarging a square orchard

MediumBrainteasers~6m

A gardener plants trees in a square array and has 146146 trees left over. To make the square one row larger in each direction, he would need 3131 more trees than he has. How many trees does he have in total?

Show hints (2)+
  1. Side kk+1k\to k+1 needs 2k+12k+1 more trees. That equals surplus ++ shortfall =146+31=146+31.
  2. 2k+1=177k=882k+1=177\Rightarrow k=88; total =882+146=88^2+146.

Answer

Reveal answer →

7890

Want the full step-by-step worked solution? It's part of Premium - along with a worked solution for every question in the bank.

Asked at: SIG, Two Sigma

Related questions