GeekDad Puzzle of the Week Answer: Stair Wars

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This week we have two answer nodes when certainly there's only one answer. Help? Image: moyogo/Flickr

It’s cold enough that rather than arks, people in greater Denver are building imperial snow walkers this weekend — which means another two days next week spent huffing the off-gassing fluorescent bulbs in the stairwell of the University of Colorado Cancer Center. How many people will I meet as I “run?” Well, that was this week’s puzzle:

Let’s imagine that everyone in the stairwell, me included, travels a constant one floor per 15 seconds, either up or down. I start from the top, eighth floor, run to tag floor #1 (the ground floor) and then immediately go back up, like hell’s own yo-yo. And during the half hour I run, everyone’s going to lunch and so they travel ONLY down the stairs — they enter at a certain floor and walk all the way to floor #1 (the ground floor), where they exit.

Here’s the tricky part: people enter the stairwell at every minute multiple of the level they enter. For example, one person enters on the 6th floor at minutes 6, 12, 18, 24 and 30 (and they walk from the 6th floor, down); likewise a person enters from the 8th floor at minutes 8, 16, and 24 — again walking down. (Fugheddabout anyone entering at the first, ground floor because that would be silly.)

How many people do I meet?

I have to admit, there was some confusion in the answer this week. Both Judd and I got 14 people — independently, we made spreadsheets split into 15-second cells and then charted the progress of our hypothetical runner up and down the stairs, and the people entering going down the stairs. A couple other people also submitted 14. Then there’s another robust answer: people are settling on 21, which they’re mostly getting by coding. (For example, Paul, who wrote this:

I checked my work and it very much seems right. Then I watched Paul’s simulation and it very much seems right. And so I believe the cat is both alive and dead at the same time! Someone’s making a consistent error — either the 14-ers or the 21-ers. What that error is, I can’t tell. If you can sort out this conundrum for me, I’d be happy to see it. Until then, I’m accepting both answers.

And the winner of this week’s $50 ThinkGeek gift certificate is the aforementioned Paul. Congrats! The rest of you can use the code GEEKDAD21FK to get $10 off a $50 order. (Okay, it doesn’t have to be exactly $50. It can be more.)

Tune in Monday when Judd drops more phat rhymes from the world of puzzlecore.

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