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I've been playing Praser 5, an old interactive fiction game (like Zork) made a few decades ago, and available here. In it, you wander from area to area solving riddles posed by mythical animals. Many of the puzzles involve lateral thinking. I've had quite a bit of difficulty with the following puzzle:

The sphinx stretches lazily and says, "Consider a Euclidean plane. Draw points O and S. Put I between them so that half the distance between O and I is the distance between O and the point one-third of the way from O to S. Say that S and I are one bloit apart. Now put D as far from O as S is from the point between I and O, so that the ratio of the distance between D and I and the distance between O and the point between D and I is twice the distance between O and the point between D and O. Mark E so that the distance between O and the point between E and the point between D and E is half the distance between O and I, and half the distance between S and E is the distance between the point between S and D and D. Now, P is placed so that the sum of the distances between P and S and between P and D, one of which is two bloits, is as long as E is far from the point three times as far from O as it is from D so that D is between that point and E. P is closer to I than it is to S, but if it weren't, H would be the point between P and D as far from where P really is as I is from where P would be. R is as far from H as O is from S and as far from D as D is from E. So what is the shape of the figure OSRHP, and what is its area in square bloits?" It smiles gently and curls up again.

So far, I have O, I, and S on a line, with O and I two bloits apart and S one bloit past I. D is two bloits above O, and E is two bloits below O.

Beyond that, I suspect that P is in the lower right, H in the upper middle, and R in the lower left. I think the result is a star/pentagram. However, to check your answer in game, you must simultaneously enter the shape and area.

Is my solution (a star) correct? And he can I find the area?

(Note: to try speaking to the Sphinx in-game, type arlumere).

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  • $\begingroup$ A bit off-topic, but since this is solved anyways: Do you have hint on the unicorn's question which seems to be related to this one? $\endgroup$ – ProGlockner Apr 8 '15 at 15:50
  • $\begingroup$ @ProGlockner unscramble the names of the points. $\endgroup$ – Brian Rushton Apr 8 '15 at 17:42
  • $\begingroup$ Oh well, that was easy... why didn't I come up looking into the points the first place... $\endgroup$ – ProGlockner Apr 9 '15 at 7:06
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Consider a Euclidean plane. Draw points O and S.

enter image description here

Put I between them so that half the distance between O and I is the distance between O and the point one-third of the way from O to S. Say that S and I are one bloit apart.

So I lies at the 1/3rd point between S and O. enter image description here

Now put D as far from O as S is from the point between I and O, so that the ratio of the distance between D and I and the distance between O and the point between D and I is twice the distance between O and the point between D and O.

D is two bloits from O, and happens to form a right triangle which satisfies the other requirements.

enter image description here

Mark E so that the distance between O and the point between E and the point between D and E is half the distance between O and I, and half the distance between S and E is the distance between the point between S and D and D.

Putting E two bloits above O works here.

enter image description here

Now, P is placed so that the sum of the distances between P and S and between P and D, one of which is two bloits, is as long as E is far from the point three times as far from O as it is from D so that D is between that point and E.

"that point" is collinear with D and E. It's three bloits from O and one bloit from D. E is five bloits from "that point", so the two distances in the first clause are two and three bloits, although we don't know which is which. So P can be in four potential places, represented here as the intersection of the red and blue circles.

enter image description here

P is closer to I than it is to S, but if it weren't, H would be the point between P and D as far from where P really is as I is from where P would be.

The only candidate P closer to S is the one farthest to the right. We call this "Fake P". I is sqrt(5) bloits away from Fake P. We'll draw circles of radius sqrt(5) around each of our other candidate P's to see if any of them intersect the line between D and Fake P. This is where H is.

enter image description here

Only one of the circles intersects with the line. That circle belongs to the candidate P that lies on top of O.

R is as far from H as O is from S and as far from D as D is from E.

Only one point is 3 units from H and 4 units from D.

enter image description here

So what is the shape of the figure OSRHP, and what is its area in square bloits?

enter image description here

The shape is a parallelogram and its area is 6 square bloits.

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  • $\begingroup$ What do you use for your diagrams? $\endgroup$ – wedstrom Mar 17 '16 at 21:30
  • $\begingroup$ @wedstrom IIRC I used Python and PIL to draw the lines / circles / points, then I added the text and numbers in MS Paint. $\endgroup$ – Kevin Mar 18 '16 at 3:11

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