Brain Teasers
Three Statements IV
Which of these three statements are true?
1. Sam received $0.41 change from a purchase. If he received 6 coins, 3 of the coins had to be dimes.
Coins in circulation are: 1 cent, 5 cents, 10 cents, 25 cents. 1 dime=10 cents.
2. If there are more inhabitants in Los Angeles than there are hairs on the head of any inhabitant, and if no inhabitant is totally bald, it necessarily follows that there must be at least two inhabitants with exactly the same number of hairs.
3. The price of a T-shirt was cut 20% for a sale. The price of the T-shirt should be increased by 25% if it is to be sold again at the original price.
1. Sam received $0.41 change from a purchase. If he received 6 coins, 3 of the coins had to be dimes.
Coins in circulation are: 1 cent, 5 cents, 10 cents, 25 cents. 1 dime=10 cents.
2. If there are more inhabitants in Los Angeles than there are hairs on the head of any inhabitant, and if no inhabitant is totally bald, it necessarily follows that there must be at least two inhabitants with exactly the same number of hairs.
3. The price of a T-shirt was cut 20% for a sale. The price of the T-shirt should be increased by 25% if it is to be sold again at the original price.
Answer
All the three statements are true.In statement 1, there must be one 1 cent because of the remainder upon division by 5. The remaining 5 coins total 40 cents, which can only be 5*2+10*3.
In statement 2, the pigeonhole principle is used, and you should know it.
In statement 3, if the original price is X, then X*(1-0.2)*(1+0.25)=X*0.8*1.25=X, which is again the original price.
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Comments
uhhhhh.....what?
May 07, 2006
It was so easy, it was hard (I thought it was a trick).
I agree with themadscientist person I thought it was a trick to until I figured out all three of them and stuff
Good one. I liike these. Give me more.
assumptions can kill - i assumed only one was right so killed myself trying to disprove each of my correct answers - ugghhh
To assume EVERYONE should know the 'pigeon hole' principle is a bit insensitive.
mm..yeah i don think everyone knows that "pigeon hole".anyways even knowing tht i failed to get it.. may b mi abstract brain side not woking rite now. hehe.
Okay, I'll admit it... I don't know the pidgeon hole principle. And not only that, but I have decided I do not agree that number 2 is correct. I do agree that 1 and 3 are totally correct, but number 2? I don't care how many inhabitants there are, I don't agree that it MUST follow that 2 will have the same number of hairs on their heads. It may be probably, but it's not a guarantee.
Now you can all go ahead and laugh.
Now you can all go ahead and laugh.
Same as Komon. Killed my brain tryring to prove two of them less correct than the others.
Scallio:
For number 2, let's pick some random numbers. Say LA has 1,000,000 residents. None of the residents has 1,000,000 hairs on their head and none has zero (as stipulated in the statement). This leaves 999,999 possibilities (ranging from one hair to 999,999 hairs). But there are 1,000,000 residents, so at least two residents must have the same number of hairs on their head.
To make it clearer, let's say that Resident 1 has 1 hair, Resident 2 has 2 hairs, Resident 3 has 3 hairs ... Resident 999,999 has 999,999 hairs. The last resident -- Resident 1,000,000 cannot have a unique number of hairs given the stipulations.
For number 2, let's pick some random numbers. Say LA has 1,000,000 residents. None of the residents has 1,000,000 hairs on their head and none has zero (as stipulated in the statement). This leaves 999,999 possibilities (ranging from one hair to 999,999 hairs). But there are 1,000,000 residents, so at least two residents must have the same number of hairs on their head.
To make it clearer, let's say that Resident 1 has 1 hair, Resident 2 has 2 hairs, Resident 3 has 3 hairs ... Resident 999,999 has 999,999 hairs. The last resident -- Resident 1,000,000 cannot have a unique number of hairs given the stipulations.
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