Problems of the Week

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2018-07-09 Basic


A ball that’s half wood and half iron rolls on a flat surface.

Which position is most likely when it comes to rest?

The three circles are identical and centered on the triangle's vertices. Two of the circles are tangent to each other.

What is the blue area?

This fun photo of two brothers with their hair standing on end was taken on the top of Moro Rock in Sequoia National Park in 1975.

The elder brother recalls the day that they hiked to the top of the rock while the weather around them worsened. Suddenly the brothers realized their hair was standing on end, and scrambled to take a photo. Just minutes later the younger boy was struck by lightning, leaving both brothers with third-degree burns.

Lightning is an amazing effect caused by negative charge accumulating at the bottom of clouds, but can be fatal; up to 24 000 people are killed each year by lightning strikes worldwide.

Why did the boys' hair stand up on end just before the lightning strike?

Story and image credit: Daily Mail

Are there positive integers (a,b)(a, b) such that

  • aa divided by bb gives remainder 6, and
  • bb divided by aa gives remainder 5?

Benjie and Esther are exploring a mansion consisting of a 5×85 \times 8 grid of rooms. Each room contains a gold coin, but the explorers are only able to move North and/or East through the rooms, entering the room marked Start and leaving through the room marked End.

If Benjie and Esther take the paths shown, they will collect 22 coins. Can they collect more?


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