Countolaf
Level 11 poster
Count Omar, the Wild Warrior
Posts: 1,113
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Post by Countolaf on May 13, 2006 23:51:36 GMT 1
1) I have 3 pairs of shoes: S1, S2 and S3. A pair is black, other is brown, and other white, not in this order. Just one of the affirmations below is correct:
- S1 is black
- S2 is not black
- S3 is not white
Which are the colours of the pairs of shoes S1, S2 and S3, in this order?
2) Ann, John, and Alex took a bus tour of Disneyland. Each of them must pay 5 plastic chips for the ride, but they have only plastic coins of values 10, 15, and 20 chips (each has an unlimited number of each type of coin). How can they pay for the ride?
3) We are given 80 coins of the same denomination; we know that one of them is counterfeit and that it is lighter than the others. Locate the counterfeit coin by using four weighings on a pan balance.
4) We have 5 keys and 5 padlocks for them. Which is the maximum number of tries we need to estabilish the correct correspondency between keys and padlocks?
5) How can I cut a cake in 8 pieces, using 3 cuts?
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Post by Novamero on May 14, 2006 2:22:25 GMT 1
1)white, black, brown
2) Use one 15 chip?
4) 14
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scotchy
Level 0 poster
The Sorcerer knight
Posts: 48
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Post by scotchy on May 14, 2006 7:10:13 GMT 1
#1 same as the guy above me
#2 they each give 5 plastic chips, since there was no value asked for except for quantity
#3 This one took me a bit: Divide the coins in 3 equal piles (27,27,26) put the 27 piles on the balance, if they equal in weight then you know the 26 pile has the counterfeit, if one is lighter you have the 27 pile. After that you can do piles of 9, 9 ,9 (second weigh) and then take the lighter pile, and divide 3,3,3 (third weighing) which will give you 3 coins, which you can weigh and find the fake one.
#4 14
#5 put the cake on its side, then cut once in half that way, then lay it back down normally and cut ---- and the | it will equal 8
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Post by Fox Mc Cloud on May 14, 2006 10:12:05 GMT 1
1) I have 3 pairs of shoes: S1, S2 and S3. A pair is black, other is brown, and other white, not in this order. Just one of the affirmations below is correct: - S1 is black - S2 is not black - S3 is not white Which are the colours of the pairs of shoes S1, S2 and S3, in this order? 2) Ann, John, and Alex took a bus tour of Disneyland. Each of them must pay 5 plastic chips for the ride, but they have only plastic coins of values 10, 15, and 20 chips (each has an unlimited number of each type of coin). How can they pay for the ride? 3) We are given 80 coins of the same denomination; we know that one of them is counterfeit and that it is lighter than the others. Locate the counterfeit coin by using four weighings on a pan balance. 4) We have 5 keys and 5 padlocks for them. Which is the maximum number of tries we need to estabilish the correct correspondency between keys and padlocks? 5) How can I cut a cake in 8 pieces, using 3 cuts? 1. S1: Black; S2: White, S3: brown 2. 2 give a chips of 15 to one and get a 10 chips back and then the guy pays with a 15 chips. 3. dunno 4. 10 times, 4 in the first, 3 in the 2nd, 2 in 3th and 1 in 4th 5. Cut it in 2 and then put both sides on eachother then cut again, put all on a pile and cut 3th time. |
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Countolaf
Level 11 poster
Count Omar, the Wild Warrior
Posts: 1,113
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Post by Countolaf on May 14, 2006 12:49:38 GMT 1
Solutions: 1 - Novamero's solution 2 - Fox's solution 3 - Ouch! It is not so simple  Scotchy's solution 4 - Fox's solution 5 - Scotchy's and Fox's solutions |
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scotchy
Level 0 poster
The Sorcerer knight
Posts: 48
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Post by scotchy on May 14, 2006 13:29:33 GMT 1
May way works on the cake Just not the way your thinking.. I think outside the box xD Also my chip solution works to, you never said how much they need to pay, you just said give 5 plastic chips |
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Countolaf
Level 11 poster
Count Omar, the Wild Warrior
Posts: 1,113
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Post by Countolaf on May 14, 2006 13:47:32 GMT 1
They don't have a coin which values 5 chips
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Post by Fox Mc Cloud on May 14, 2006 16:18:02 GMT 1
May way works on the cake Just not the way your thinking.. I think outside the box xD Also my chip solution works to, you never said how much they need to pay, you just said give 5 plastic chips They have to pay 5 chips and not 5 chipses  . |
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scotchy
Level 0 poster
The Sorcerer knight
Posts: 48
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Post by scotchy on May 14, 2006 19:53:37 GMT 1
Just admit my cake solution works too and im good to go xD
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Post by Fox Mc Cloud on May 14, 2006 20:58:25 GMT 1
Yea altought I would not like to eat from your cake ;D.
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Post by elpancho81 on Jul 12, 2006 18:36:59 GMT 1
scotchy is right. The problem says that they have to pay 5 CHIPS, not a CHIP of value 5. The problem is not redacted in a correct way because it misleads a lot.
The problem with the coins can be done in another way. Make piles of 20, the one weighing less has the wrong chip. Then divide the chips in piles of 5. Then divide the pile that weighs less in 2,2,1. If the pile of 2 weighs the same, the fake one is the remaining one. Else, you take the pile weighing the less and weigh a chip. Take the total amount of the third weigh and substract the four weigh. If you get a result higher than the half of the third amount, then the fake one is the one you didn't weigh.
There's no unique solutions, only different choices.
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Post by Fox Mc Cloud on Jul 12, 2006 21:18:22 GMT 1
It are coins, no chips.
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