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So another day!
Yesterday's puzzle was solved by raiame and datscilly, as they literally posted within 1 minutes of each other. Good job!
+ Show Spoiler [solution] +
Number each color 0 to n-1. Give each prisoner a pre-determined number-sum modded n. So each prisoner would have a mod-sum ranging from 0 to n-1. When a prisoner sees all other guy's hat, he adds all other guy's hats color together, and mod it with n. He then takes that out of his pre-determined sum, and say that the difference is his own hat.
This works because as long as the prisoner can guess the total sum correctly, subtracting the other guy's hat sum will give his own hat color.
The total number of sums possible mod_n is n numbers, and since each prisoner guess a pre-determined sum from 0 to n-1, one will match the total sum and therefore one would have the right answer for his own hat color.
Day5's puzzle:
I'll give something simple today...
A vendor sells toys, he buys the toys for $18 and sells them for $21. One day, a kid walks in and hands him $100 bill, since he does not have change, he walks to his neighbor, and breaks up the $100 bill(i.e. he gives neighbor the $100 bill, and his neighbor gives him $100 worth of smaller bills).
He then proceed to give the kid his toy and change for the purchase.
Soon his neighbor was back, "Your 100$ bill was fake!", The neighbor said, and demanded his $100 back. So the vendor gives $100 to his neighbor.
How much money did the vendor lose as a result of this transaction?
Extra:
Again, put answer in spoilers, clarification will be given(unlikely for this puzzle).
Difficulty Poll:
This is something I'd like to try for fun, just try to vote honest.
Poll: How difficult is this puzzle?
(Vote): Can't do it
(Vote): Think I have it
(Vote): Sure I did it right
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+ Show Spoiler +assuming buying the toy for 18 dollars isn't counted in the transaction, 79 for change to the boy and 100 paid to the neighbor afterward, the kid never actually paid anything, so 179? if buying the toy is counted, then 197?
edit oh wait shit rofl the neighbor gave him a legit 100 so subtract 100 of lost money, 79 (not counting originally purchasing toy)/97 (counting it)?
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Editting answer.
+ Show Spoiler +Forgot the kid's bill was fake and misunderstood the question  . The profit from the neighbor is $21, excluding the change he gives to the boy. The shopkeeper then has to give $100 back to the neighbor. He also lost the toy, so it would be -18+21-100, which would be $97 lost.
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On May 01 2009 15:33 Ichigo1234551 wrote:+ Show Spoiler +100 dollars because he gave the money back to his neighbor
+ Show Spoiler +full explanation please? o.O are you counting the fact that the change for the kid was 79?
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On May 01 2009 15:37 SpiritoftheTunA wrote:+ Show Spoiler +full explanation please? o.O are you counting the fact that the change for the kid was 79?
+ Show Spoiler +Its a trick question yo. He only asks us about the transaction that he gave the money back to his neighbor.
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On May 01 2009 15:40 Ichigo1234551 wrote:Show nested quote +On May 01 2009 15:37 SpiritoftheTunA wrote:On May 01 2009 15:33 Ichigo1234551 wrote:+ Show Spoiler +100 dollars because he gave the money back to his neighbor + Show Spoiler +full explanation please? o.O are you counting the fact that the change for the kid was 79? + Show Spoiler +Its a trick question yo. He only asks us about the transaction that he gave the money back to his neighbor.
+ Show Spoiler +no i think you're just picking the wrong antecedent for "this transaction"
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+ Show Spoiler +197, spent $18 on the toy, gave the kid $79 of real money as change and gave his neighbor $100 real money
edit
wait thats wrong haha
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+ Show Spoiler +-18 for buying toy. +0 from fake money. +100 from neightbour. -79 from giving change. -100 from repaying neighbour. So lost $97 total.
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+ Show Spoiler +Where is everyone getting $118? At least explain your answer guys? lol.
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On May 01 2009 15:44 deathgod6 wrote:+ Show Spoiler +Where is everyone getting $118? At least explain your answer guys? lol.
seconded
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Whoops, revised it.
+ Show Spoiler ++21 selling to the kid
-18 for cost of toy
-100 for giving to neighbor
so he lost 97 dollars.
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+ Show Spoiler +He lost 97 dollars. His profit margin was $3. The transaction between the kid and his neighboor and stuff is all irrelevent. He still made 3 dollrs. Then the neighboor wanted 100 dollars back. So the earnings 3 minus 100 dollar is - 97. He lost 97 dollars.
and how did you guys voted in poll without before evan posted the correct answer is beyond me...
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+ Show Spoiler +As ktp posted the transaction with the neighboor is irrelevent. Think that there was no neighbor and the vendor had the change. Boy comes in gives nothing picks change (-79) and leaves with the toy (-18). Total: lose 97 doll.
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-79 for the change he gave the kid back
-18 for the cost of the toy
-100 for the money he gave the vendor
so 197
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Use spoilers+ Show Spoiler +On May 01 2009 16:53 Ichigo1234551 wrote:
-79 for the change he gave the kid back
-18 for the cost of the toy
-100 for the money he gave the vendor
so 197 -197+ 100 from neighbor= -97
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On May 01 2009 17:02 Malongo wrote:Use spoilers + Show Spoiler +On May 01 2009 16:53 Ichigo1234551 wrote:
-79 for the change he gave the kid back
-18 for the cost of the toy
-100 for the money he gave the vendor
so 197 -197+ 100 from neighbor= -97
+ Show Spoiler +You do know that the "+100 from neighbor" you have posted is the fake 100? So he actually does lose 197
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On May 01 2009 19:01 kOre wrote:Show nested quote +On May 01 2009 17:02 Malongo wrote:Use spoilers + Show Spoiler +On May 01 2009 16:53 Ichigo1234551 wrote:
-79 for the change he gave the kid back
-18 for the cost of the toy
-100 for the money he gave the vendor
so 197 -197+ 100 from neighbor= -97 + Show Spoiler +You do know that the "+100 from neighbor" you have posted is the fake 100? So he actually does lose 197
+ Show Spoiler +The fake 100 is from the boy not the neighbours
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+ Show Spoiler +
-18 -> cost of toy
+100 -> the money his neighbor gives
-79 -> change to the kid (real $).
-100 -> the money he gives back to neighbor
-----
-97
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+ Show Spoiler +-18 for purchasing the toy. Then he gives 79 back to the kid. Which leaves him with 21. Now he got to give back the 100$. So its 21-100-18= -97
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+ Show Spoiler +97 dollars, but I thought about it a little differently. Remember the kid gets smaller bills from the neighbor, so when he buys the toy ideally he gets no change back, but the point is he pays with real money. Vendor makes 3 dollars, but then has to lose 100 dollars to the neighbor.
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as a math major, i have to say that the question is painfully imprecisely worded
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+ Show Spoiler +
He lost $79 from the transaction.
Whether or not the kid ever walked into the shop is irrelevant to his original purchase of $18
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On May 01 2009 22:53 Day[9] wrote:
as a math major, i have to say that the question is painfully imprecisely worded
I can't imagine this being hard to understand.
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+ Show Spoiler +start
lender vendor boy
(100) (100+toy) (100f)
end
lender vendor boy
(100) (21 + 100f) (79+toy)
It's a closed system so we can just look at the beginning and the end. The lender's money doesn't change so he's ignored. Since the boy gains 79 + toy the vendor must have lost 79 + toy which equates to 97. This makes since because all the vendor is really out is the fake hundred plus the difference in the toy's buy/sell price.
edit-made numbers easier to tell apart.
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just read the op so far
we assume the child with $100 buys as many toys as he can with the $100, as all children would, or 1, which i assume is more likely intended.
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On May 02 2009 01:51 inReacH wrote:Show nested quote +On May 01 2009 22:53 Day[9] wrote:
as a math major, i have to say that the question is painfully imprecisely worded I can't imagine this being hard to understand.
Pretty sure you don't think about it like a math major.
+ Show Spoiler +The tricky part is "this transaction," which as written could refer to any of the total net loss the toy plus the fake 100, the loss from just the trades with the neighbor, or the loss just from being forced to give 100 back to the neighbor. The math is trivial in all cases and the problem is unclear as to the definition of the transaction, so honestly this isn't a math problem at all, but more of a literature problem of "what did the author actually mean."
That said, to me the most natural interpretation of "transaction" here would be exchanging money with the boy and then having to give money back to the neighbor. The original cost of the toy was paid at a another time, a sunk cost, and wouldn't count for this. Thus, I would consider his loss for "this transaction" as $79. I'd say the people saying $97 have nearly as good an argument, though.
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EPT
