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The Ultimate YuGiOh! Deck at a Bargain Price

October 27, 2008

At breakfast school, I asked James — the YuGiOh maniac — the following hypothetical question. As you’ve guessed, I’m a sadistic mom, and I’m in some danger of becoming a born-again math lover.

I asked, “Suppose someone offered to sell you the ULTIMATE YuGiOh! Deck — a copy of every known card INCLUDING THE ULTRA RARE CARDS. This is what you’d have to do. On the first day of next month, November, you have to pay one penny. The next day, double that and pay two pennies. Then four pennies, and so forth. Then on the last day of the month, you make the last payment, and you get the deck. Do you think that would be a good deal?”

“Hmmm … all real cards? No fakes?”

“Yep. All real.”

All the YuGiOh cards?”

“Every one.”

“That WOULD be a good deal. I think I saw a deck kind of like that on e-bay for — like — $1000. And this is going to come to about $5.”

Sarah, who is wise to my tricks, said, “No. I don’t think so.” But James, who is a virgin when it comes to the concept of exponential growth, persevered.

“Well … it’ll come to about $40. That’s still a good deal!”

So, how much would this apocryphal deck cost? We laid pennies on each square of a November calendar … 1 penny on the 1st, 2 pennies on the second, 4 pennies on the third, 8 pennies on the fourth, 16 pennies on the fifth … then we switched to using a calculator.

Sarah and James are hard at work, in the other room, working on solving the problem. Any of you mathy types want to take a stab at it? (And, yes, of course it’s legal to use a calculator.) How much would the deck cost, or to simplify it, how much would the final payment be?

Well … his official answer is “I ain’t payin’ that much!”

here’s what we came up with:

Day 1 — 1 penny
Day 2 — 2 pennies
Day 3 — 4 pennies
Day 4 — 8 pennies
Day 5 — 16 pennies
Day 6 — 32 pennies
Day 7 — 64 pennies
Day 8 — $1.28
Day 9 — $2.56
Day 10 –$5.12
Day 11 — $10.24
Day 12 — $20.48
Day 13 — $40.96
Day 14 — $81.92
Day 15 — $163.84
Day 16 — $327.68
Day 17 — $655.36
Day 18 — $1310.72
Day 19 — $2621.44
Day 20 — $5242.88
Day 21 — $10,485.76
Day 22 — $20,971.52
Day 23 — $41,943.04
Day 24 — $83,886.08
Day 25 — $167,772.16
Day 26 — $335,544.32
Day 27 — $671,088.64
Day 28 — $1,342,177.28
Day 29 — $2,684,354.56
Day 30 — $5,368,709.12

Grand Total — $10,737,418.19 — The bargain price of around ten million dollars. Hey — it would be cheaper than the great bail-out debacle.

Books Relating to This Topic:

The King’s Chessboard by David Birch

One Grain Of Rice: A Mathematical Folktale by Demi

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