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2017-08-07 Basic

         

\[\Large 0 = 1\ \square\ 2\ \square\ 3\ \square\ 4\ \square\ 5\ \square\ 6\ \square\ 7\ \square\ 8\ \square\ 9 \]

Can you fill the boxes with \(+\) and \(-\) to make this equation true?

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Pi Han Goh by Pi Han Goh

\(6\) is divisible by \(6\).
\(6\times6\) is divisible by \(6+6\).
\(6\times6\times6\) is divisible by \(6+6+6\).

Is it true that \(\underbrace{6\times6\times\cdots\times6}_{n\text{ times}} \) is divisible by \(\underbrace{6+6+\cdots+6}_{n\text{ times}} \) for all positive integers \(n\)?

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Pi Han Goh by Pi Han Goh

The drops from a leaky faucet form a steady wave in the water, a snapshot of which is shown in the diagram above.

Rob carefully lowers his paper boat into the water such that it starts at the bottom of the wave.

True or False?

Rob's boat will move away from the faucet along with the ripples.

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Pranshu Gaba by Pranshu Gaba

\[\large \begin{matrix} &&& & & \square \\ &&& & \square & \square \\ + & & & \square & \square & \square \\ \hline \\ & & 1 & 1 & 1 & 1 \end{matrix} \]

Each box contains a non-zero digit, not necessarily distinct from other numbers. Is the equation above possible?

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Christopher Boo by Christopher Boo

The store has 6 flavors of ice-cream. Each of 6 friends likes exactly 4 flavors.

Is there guaranteed to be a flavor which at least 4 friends like?

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Agnishom Chattopadhyay by Agnishom Chattopadhyay
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