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Ponder This

April 2000

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Ponder This Challenge:

We have decided to revamp the tax code in a major way. All residents will line up, left to right, with Sam standing at the far left at position 0 and the rest of us in positions 1, 2, 3, etc. On January 1 of each year, each resident will observe the net worth of the person on his left. On April 15, this resident pays that much in tax out of his own pocket. (So if Jack is at position 20 and Amanda at position 19, on April 15 Jack will pay the amount that Amanda had on January 1.)

"But what if I don't have that much money?"

Just run a deficit. Does that bother you?

"But what if my neighbor is running a deficit on January 1?"

If your neighbor was running a ten dollar deficit on January 1, then on April 15 you give the government a ten dollar deficit. That's the same as if the government pays you ten dollars.

Sam: "I don't have a neighbor, since I'm at position 0."

That's okay, Sam, you alone don't have to pay taxes. Just pretend your non-existent neighbor has zero net worth.

"What if people change places, drop out, come into the system...?"

None of that is allowed. Furthermore, no money ever changes hands except for payment of taxes. Okay, no further questions.

"Wait, wait. Why are we doing a US-centric April 15 tax day, if IBM is an international company?"

I said no further questions.

Sam starts out with one dollar, and the rest of you start with varying amounts. Some of you will start with no money, in particular the four people on the far right-hand end of the line will be broke. Some of you might even start with deficits.


Four years pass. At the end of those four years, Sam still has his one dollar, and the only other people with nonzero net worth are at positions q, r, s and t, with q < r < s < t. Here q,r,s,t are unknown integers, not assumed to be consecutive, and the answer to the problem will involve only the values q,r,s,t.

How much did the government collect in the first year (net)? (That is, collections minus payouts.)

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Challenge: 04/01/00 @ 12:00 AM EDT
Solution: 05/01/00 @ 9:00 AM EDT
List Updated: 04/20/00 @ 9:00 AM EDT

People who answered correctly:

Joseph DeVincentis (4.4.2000 @ 4:55 PM EDT)

Jimmy Hu (4.4.2000 @ 8:25 PM EDT)
Dave Biggar (4.4.2000 @ 11:04 PM EDT)
Peter Berghmans (4.5.2000 @ 5:40 PM EDT)
Vidya Sagar (4.7.2000 @ 9:01 AM EDT)
Amos Guler (4/10 at 2:56 PM EDT)
David MacMahon (4/10 at 7:02 PM EDT)
Mihai Cioc (4/12 at 2:02 PM EDT)
Jessica Lang Jones (4/13 at 4:16 AM EDT)
Tim Edmonds (4/17 at 5:41 AM EDT)
Frankie Dintino (4/17 at 11:15 PM EDT)
Tao Lin (4/18 at 11:50 PM EDT)

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