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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