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Story:

You go to a restaurant called "Likeable Alb's" to eat some of their world-famous chips. You sit down in your chair. Some time later, the waiter comes and hands you the menu. The menu contains how much money it will cost to buy certain amounts of chips. "Alright then" you say, as you look at the menu. The menu reads as the following:

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1 chip for $1

5 chips for $5

25 chips for $15

80 chips for $40

400 chips for $100

900 chips for $250

2,000 chips for $500

10,000 chips for $1,500

We will, though, give you any amount of chips, as long as it's between 1 and 10,000, and it will be a specific price that we can calculate for you.

$------------------------------------$

You decide that you don't want to have any of these. You want 300 chips, so that's what you order. The chips are delicious, but when you finally get the bill, you look at the cost and are very confused.

Problem:

When you looked at your bill, what made you so confused? Why?

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  • $\begingroup$ Your bill could have been anything. The menu didn't state how much it would be if you ordered 300, only how much it would be for the specified numbers. $\endgroup$ – Illyasviel Nov 4 '15 at 23:23
  • $\begingroup$ There, I added something to help with the confusion. $\endgroup$ – Xandawesome Nov 4 '15 at 23:25
  • $\begingroup$ Why did someone downvote this? I'm curious... $\endgroup$ – Xandawesome Nov 4 '15 at 23:41
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    $\begingroup$ Is "Likeable Alb's" a hint towards the answer? I cannot see one myself, but I'm curious if there is. $\endgroup$ – Ken Y-N Nov 5 '15 at 9:11
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    $\begingroup$ The phrase "Likeable Alb's" is an anagram... Which is a hint to the actual answer. Try it out! $\endgroup$ – Xandawesome Nov 6 '15 at 0:15
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The price is

\$1 per chip, but the money is listed in base 20.

When your bill comes out to

\$F0

of course you're confused!

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  • $\begingroup$ Correct! You got it pretty fast! $\endgroup$ – Xandawesome Nov 4 '15 at 23:33
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$300 = 80 \times 3 + 25 \times 2 + 5 \times 2$

So it might have cost him $40 \times 3 + 15 \times 2 + 5 \times 2 = 160$, which is more than what he would have paid had he ordered $400$ chips.

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  • $\begingroup$ No, sorry, but nice try! How'd you get the equations though? $\endgroup$ – Xandawesome Nov 4 '15 at 23:14
  • $\begingroup$ @Xandawesome It is just trying to make 300 from the list of numbers given from highest possible value that can fit into 300 to lowest. hence 80 * 3 + 25 * 2 + 5 * 2 $\endgroup$ – Yaze Nov 5 '15 at 0:22
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Since you didn't order 400 chips, they didn't charge you the 400 chip price, they charged you the 1 chip price (\$1) 300 times. Therefore your bill was \$300.

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