# Problems of the Week

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# 2017-12-18 Basic

Is cell Z a mine?

Note: The number in each of the 4 open cells represents the number of hidden mines in the 8 cells around that number.

1 is divisible by 1.
$$2\times 3$$ is divisible by 2.
$$4\times5\times6$$ is divisible by 3.
$$7 \times 8 \times 9 \times 10$$ is divisible by 4.
$$11 \times 12 \times 13 \times 14 \times 15$$ is divisible by 5.

True or False?

The product of any $$N$$ consecutive integers must be divisible by $$N.$$

Stars in the night sky twinkle, but planets do not.

Why?

Nine identical circles are symmetrically fitted into a square, as shown.

What is the ratio of the red area to blue?

A biologist is searching for a rare frog in a remote region of Brilliantia. The local villagers claim a single frog lives in a series of four ponds.

They claim that the frog stays in a pond during the day, and moves to a neighboring pond every night. The biologist can only check one pond a day, and she does not impact the frog's movement at night.

Can the biologist devise a strategy that guarantees she eventually discovers the frog?

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