All entries for Monday 09 November 2009

November 09, 2009

Target Practice

Target Practice

Robin Hood and Friar Tuck were engaging in some target practice. The target was a series of concentric rings, lying between successive circles with radii 1, 2, 3, 4, 5. (The innermost circle counts as a ring.)

Friar Tuck and Robin both fired a number of arrows.

“Yours are all closer to the centre than mine,” said Tuck ruefully.

“That’s why I’m the leader of this outlaw band,” Robin pointed out.

“But let’s look on the bright side,” Tuck replied. “The Total area of the rings that I hit is the same as the total area of the rings you hit. So that makes us equally accurate, right?”

Naturally, Robin pointed out the fallacy...but:

Which rings did the two archers hit? (A ring may be hit more than once, but it only counts once towards the area.)

For a bonus point: what is the smallest number of rings for which this question as two or more different answers?

For a further bonus point: if each archer’s rings are adjacent – no gaps where a ring that has not been hit lies between two that have – what is the smallest number of rings for which this question has two or more different answers?

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