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## Question

Hillary took a trip to Washington D.C. to see the sites. Here's two questions about her trip. See if you can figure them out.

1) Hillary found herself in such a place that she was between the Washington Monument and Lincoln Memorial, but could see the reflecting pool, the Washington monument, and the Lincoln memorial all simultaneously unaided and without moving her head. Where must she have been?

2) Hillary approached the pentagon from an unknown direction. Which is more likely, that she saw 2 walls or 3?

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In a helicopter????

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she was standing at the Lincoln Memorial, looking into the reflecting pool, seeing a reflection of the Washington Monument. There was also a penny in the reflecting pool which shows the Lincoln Memorial on the back.

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2) Hillary approached the pentagon from an unknown direction. Which is more likely, that she saw 2 walls or 3?

I think it is 2 walls would be more likely to see than 3 walls if you took a 360 degree view of it

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Let me see if I can explain this. Your angle of approach to the Pentagon will determine how many walls you can see. Based on where you in relation to the rays in the diagram, you could see one, two, or three walls. Since "Area 1" is not an approaching path, we can disregard it for this problem. Therefore when approaching, you will see either 2 or 3 walls, as the questions states. Comparing the size of the angle for Area 3 with the combined size of the angles for the two Area 2s tells us that there is a 1/9 chance of seeing three walls as you approach. (36/(144+144+36))

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1. helicopter - although technically only your shadow [at noon] is between the two monuments.

2. This has a bunch of answers:

[a] at infinity, 2 and 3 sides are equally probable, alternating every 36 degress of approach direction

at a great [but finite] distance, it favors 2, slightly, and more so as the distance decreases.

[c] coming closer, you get to a point where 3 sides are never seen; 2 sides are seen from every angle.

[d] coming closer still, it changes, with angle of approach, from 1 side to 2 sides, favoring 2 sides.

[e] adjacent to the pentagon, 1 side and 2 sides are seen alternately every 36 degrees.

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I think Bona's right on with his "even odds" answer. Of course as you approach and get closer, you don't "see the forest for the trees" so to speak, so we assume we approach from a distance. Every 36 degrees you change viewing angle, so if you angle of approach is random, you have a 1/1 chance of seeing 2 or 3 walls.

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for #1...hillary could be in the lincoln memorial gift shop :D

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