Problems of the Week

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2018-05-21 Basic

         

In a modified version of tic-tac-toe, the middle square is blocked from play.

If this game is played optimally, who will win?

A container of water and a pump weigh 100 kg at rest. Then, the pump is switched on and sucks the water to \(\SI{1}{\meter}\) high, releasing it back into the container. This flow is steady with no spills.

What does the scale read while the water is running?

The combined area of the blue triangles is 25, and the five red squares are identical.

What is the area of the entire shape?

Charlotte selected a subset out of the integers from 1 through 20 inclusive. None of the numbers in the subset is double another number in the subset.

What is the greatest number of integers she could have selected?

In this brick puzzle, the value of a brick must be the sum of the two bricks below it:

What is the value of the top brick?

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