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#84 Squarebot

”What’s that you are holding, Squarebot?”

��ٱ�ܲ�����.”

I have met Squarebot before and am suspicious. “Are you sure, squarebot? I can see it must be a rectangle, because you have drawn it on squared paper. But I can’t count the squares without breaking social distancing rules. How wide is it?”

“16.”

“And its height?”

“16.”

“Sounds like a square, then. Just to check: what is its area?”

“289.”

“Hold on, that doesn’t work: 289 is 17 squared. You are rounding every numerical answer you say to the nearest square number, aren’t you? And if the answer isn’t a number you just say ‘Square’?”

��ٱ�ܲ�����,” chuckles Squarebot.

“So the width might actually be 17? Or 18? Or 15? Or even 20?”

��ٱ�ܲ�����,” grins Squarebot.

Can you think of a question to ask Squarebot to find out if the rectangle really is a square?

Answer next week

#83 Albatross

Solution

If we call the height of the mast 3H, the stone climbed H above that to be 4H above the ground at its peak. A parabola is a “square” function, so the height increases with the square of the horizontal distance. If the top of the stone’s path was d from the mast, Pugwash was 2d from the peak. The flight of the stone is symmetrical around the peak, so if the peak is d from the mast, it is also d from the point of impact. So the point of impact is d from the peak, 2d from the mast and 3d from Pugwash, and the stone was travelling at 3/2 or 1.5 times the horizontal speed of the albatross, or 15 knots.