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Topic: Brain Teasers and Algebra Riddles (Read 4082 times) |
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Rusty Shackleford
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couple of these i don't get
1A. Each child in a family has at least 5 brothers and 4 sisters. What is the smallest number of childern the family might have?
If correct ask again
1B. Each child in a family has at least 5 brothers and 4 sisters. What is the smallest number of children the family might have?
2. A number of chilidren are standing in a circle. They are evenly spaced and the 7th child is directly opposite the 16th child. How many children are there altogether?
3. There is a pole in a lake. One-half of the pole is in the ground, another one-third of it is covered by water, and 9ft is out of the water. What is the total length of the pole in ft?
4. Man Wrinkle spent one-fourth of his life as a boy, one-eighth as a youth, and one-half as an active man. If Man Wrinkle spent 8 years as an old man, then how many years did he spend as an active man?
5. Dad gives you money everyday to put in a new piggy bank. He gives money to you in a way that the money in the piggy bank doubles with each passing day.
If you already have 1 cent in the piggy bank and Dad gives you 1 cent the first day, 2 cents the second day, 4 cents the third day and so on, then your piggy bank gets full on the 9th day.
On which day will your piggy bank be half-full?
For example, type 6 if your answer is the 6th day.
5B. In addition to Dad's contributions, if Mom also gave you 1 cent the first day, 2 cents the second day, 4 cents the third day and so on, then on which day would your piggy bank be half full?
6. Mr.Brown has 6 black gloves and 8 brown gloves in his closet. He blindy picks up some gloves from the closet. What is the minimum number of gloves Mr. Brown will have to pick up to be certain to find a pair of gloves of the same color?
7. Suppose 8 monkeys take 8 minutes to eat 8 bananas. How many munutes would it take 2 monkeys to eat 2 bananas?
8. A 25x25 square metal plate needs to be fixed by the carpenter on to a wodden board. The carpenter uses nails all along the edges of the square such that there are 26 nails on each side of the square. Each nail is at the same distance from the neighboring nails. How many nails does the carpenter use?
9. Your teacher has a total of 16 chalks. When a chalk reduces to 1/4 of the original size, it gets too small for her to hold for writing and hence she keeps it aside. But your teacher hates wasting things and so, when she realizes that she has enough for these smail peices to join and make another chalk of the same size, she joins them and uses the new chalk stick. If she uses one chalkd each day, how many days would the 16 chalks last?
Hint: The chalks that are made by joining pieces together will again leave behind pieces!
P.S. if possible provide explanations please
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Veggie-Trunks
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Re: Brain Teasers and Algebra Riddles
« Reply #1 on: Jul 13th, 2005, 11:51pm » |
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1. I believe it is 6 boys and 5 girls. If That way there are four sisters and five brothers to every child. If it were just 9 children (4g &5b), the girls would have 5 brothers but three sisters and the boys would have 4 sisters but 4 brothers as well.
You asked the same question for the second part of that o.O.
2. I'm gonna take a wild guess and say 21 :S. Added 16 and 7 and if there's 20-21 in the group, I figure 7 will be across from 6 because 1 will be across from like 9 or 10.
3. Umm...I'm terrible at this but I figure 51. I took 1/3 and 1/2 of 100 (50 and 33), added them, then subtracted that number from 100 and got 17, which would be what's seeable. Then I just took half of every number I got (which would be 9, 17, and 25) and added them together.
That's probably some wild thinking though.
4. Well I'm thinking he couldn't have spent more than 10 years or so as a child so I'm thinking 8 is about 1/4. So I'd say he was maybe an active man for around 16 years...didn't really get this one.
5A. I'll count the days on here for ya:
1 - .1
2 - .2
3 - .4
4 - .8
5 - .16
6 - .32
7 - .64
8 - 1.28
9 - 2.56
So, obviously, the day that it would be half full is the 8th day because the total amount is the 9th day and the 8th day is half.
5B. I'm thinking the same as the first one since it doesn't change the fact that the 8th number is half of the 9th one in any case.
6. Three is all he needs to pick up. If there are only two different colors, there is no way possible he could pick up three different colors. He could of course look instead of just grabbing for something 
7. 8 minutes. Just because there are more monkeys doesn't mean they take any less time to individually eat a banana. They aren't eating them together.
Okay, let's phrase it a different way. One monkey takes 8 minutes to eat 8 bananas or 1 minute to eat one banana. It would then seem logical to say it would only take it 2 minutes to eat two because they take a minute each.
I'd rather go with my first answer but it might actually be 2 this time...
8. 100. All the sides are sharing the end nails with two other sides. This means that there are 8 nails being counted (take two from each 26 nails) when there is actually only four nails there.
9. 21. The first 16 she uses turns into four. Then those four that leave a 1/4 turn into one, then that one turns into 1/4 which is unusable. So the days she can use a piece of chalk is 21, but she actually has 21 1/4 in the end but just 21 used.
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markr
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Re: Brain Teasers and Algebra Riddles
« Reply #2 on: Jul 14th, 2005, 12:04am » |
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1B) There must be 6 boys and 5 girls because each boy has 5 brothers (for a total of 6 boys), and each girl has 4 sisters (for a total of 5 girls).
2) Since there are 8 (16-7-1) children between them on one side, there must be 8 between them on the other side. 8+8+2=18
3) 1/2 + 1/3 = 5/6 Therefore, 9ft represents 1/6 of the length. The pole is 54ft.
4) Similarly, 1/4 + 1/8 + 1/2 = 7/8 Therefore, 8 years represents 1/8 of his life. So, he lived 64 years. Half of 64 is 32.
5) If it doubles every day, and it's full on the last day, then it must have been half full the previous day.
5B) Each day, you're getting twice as much money as in the previous problem. This pulls things in by one day.
6) If the first two don't match, then the third must match one of them.
7) You get one banana per monkey each 8 minutes. Therefore, you'll get N bananas from N monkeys in 8 minutes.
8 ) 26 nails/side * 4 sides = 104 nails, but the 4 nails on the corners were each counted twice. 100 nails were used.
9) This depends on what "uses one chalk each day" means.
If she uses one chalk until it becomes too small (really 3/4 of a chalk per day) then:
after 16 days, she'll have 16 * 1/4 chalks=4 chalks
after 20 (4 more) days, she'll have 4 * 1/4 chalks=1 chalk
after 21 days (1 more), she'll have 1/4 of a chalk
If she uses one chalk's worth of chalk each day then:
after 12 days, she'll have 16 * 1/4 chalks=4 chalks
after 15 (3 more) days, she'll have 4 * 1/4 chalks=1 chalk
after 15.75 days (.75 more), she'll have 1/4 of a chalk
I suspect the first interpretation is what was intended.
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| « Last Edit: Jul 14th, 2005, 12:08am by markr » |
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Grimbal
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Re: Brain Teasers and Algebra Riddles
« Reply #3 on: Jul 14th, 2005, 12:37am » |
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1b) Considering that a condition on "every child" is true if there is no child, the minimum is 0 child (or is it 0 children?).
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towr
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Re: Brain Teasers and Algebra Riddles
« Reply #4 on: Jul 14th, 2005, 2:16am » |
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| hidden: | 1A) 11, each brother has at least 5 more brothers, each sister at least 4 more sisters, so 6+5=11
1B) 0 Quantification over an empty domain is always true. Each nonexisting creature is a flying pig
2) 18, (16-7=9 is half a circle)
3) 9*6=54
4) 32 (1/8th = 8 years -> 1/2 = 32)
5A) 8th (doubles each day, so 9th=full --> 9th-1 = half full)
5B) contradiction with 'also', dad wouldn't be doubling the content each time anymore
aside from that, still 8th day (1 cent short the day before)
6) 3, 2 if pairs are tied together
7) 8, each monkey eats a banana in 8 minutes (assuming all monkeys are equal, which in fact they're not)
8) 100 (4 x 26 - 4)
9) (16-1/4)/(3/4) = 21
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| « Last Edit: Jul 14th, 2005, 2:21am by towr » |
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Wikipedia, Google, Mathworld, Integer sequence DB
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raprap
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Re: Brain Teasers and Algebra Riddles
« Reply #5 on: Jul 15th, 2005, 3:24am » |
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1A. Each child in a family has at least 5 brothers and 4 sisters. What is the smallest number of childern the family might have?
If correct ask again
1B. Each child in a family has at least 5 brothers and 4 sisters. What is the smallest number of children the family might have?
In both cases 11. There are six boys and 5 girls. Any boy has five brothers and sisters. Any Girl has six brothers and Four Sisters.
2. A number of chilidren are standing in a circle. They are evenly spaced and the 7th child is directly opposite the 16th child. How many children are there altogether?
18 in the circle 2*(16-7)=2*9=18
3. There is a pole in a lake. One-half of the pole is in the ground, another one-third of it is covered by water, and 9ft is out of the water. What is the total length of the pole in ft?
x/2+x/3+9=X
x/6=9
x=54
length of plow is 54 feet
4. Man Wrinkle spent one-fourth of his life as a boy, one-eighth as a youth, and one-half as an active man. If Man Wrinkle spent 8 years as an old man, then how many years did he spend as an active man?
Same problem, with a wrinkle
x/4+x/8=x/2+8=x
x/7=8
x=56
x/2=28
Wilson’s life as an active man lasted 28 years
5. Dad gives you money everyday to put in a new piggy bank. He gives money to you in a way that the money in the piggy bank doubles with each passing day.
If you already have 1 cent in the piggy bank and Dad gives you 1 cent the first day, 2 cents the second day, 4 cents the third day and so on, then your piggy bank gets full on the 9th day.
On which day will your piggy bank be half-full?
For example, type 6 if your answer is the 6th day.
It doubles every day so on the 8th day it’s half full.
5B. In addition to Dad's contributions, if Mom also gave you 1 cent the first day, 2 cents the second day, 4 cents the third day and so on, then on which day would your piggy bank be half full?
The bank fills twice as fast. So the 7th day the piggy bank is half full.
6. Mr.Brown has 6 black gloves and 8 brown gloves in his closet. He blindy picks up some gloves from the closet. What is the minimum number of gloves Mr. Brown will have to pick up to be certain to find a pair of gloves of the same color?
Two possibilities, pair of brown socks, pair of black socks
BrBrBr P(e)=8/14*7/13*6/12
BlBlBl P(e)=6/4*5/3*4/12
BrBlBl P(e)=8/14*6/13*5/12
BrBlBr P(e)=8/14*6/13*7/12
BrBrBl P(e)=8/14*7/13*6/12
BlBrBr P(e)=6/14*8/13*7/12
If you sum the probabilities. P(e)=1 and if you look at the individual combos you always have, at least, a pair of one kind or another.
7. Suppose 8 monkeys take 8 minutes to eat 8 bananas. How many m1nutes would it take 2 monkeys to eat 2 bananas?
A monkey takes 8minutes to eat a bananna. Two monkeys will take 8 minutes to eat two bananas.
8. A 25x25 square metal plate needs to be fixed by the carpenter on to a wooden board. The carpenter uses nails all along the edges of the square such that there are 26 nails on each side of the square. Each nail is at the same distance from the neighboring nails. How many nails does the carpenter use?
Let A,B,C,D be the number of nails on a side. Let A∩B be the nail that is in common on the corner of side A & B, Same for B ∩C, C∩D, and D∩A. So
A+B+C+D-A∩B-B ∩C-C∩D-D∩A=4*26-4=100 nails
9. Your teacher has a total of 16 chalks. When a chalk reduces to 1/4 of the original size, it gets too small for her to hold for writing and hence she keeps it aside. But your teacher hates wasting things and so, when she realizes that she has enough for these small pieces to join and make another chalk of the same size, she joins them and uses the new chalk stick. If she uses one chalk each day, how many days would the 16 chalks last?
Hint: The chalks that are made by joining pieces together will again leave behind pieces!
For 15 days the teacher uses a piece of chalk, leaving a quarter of a stick at the end of the day. The night of the 15th the teacher joins the quarter sticks into four pieces of chalk (16/4=4). So four more days, leaving a quarter stick at the end of each day. On the night of the 20th the four quarter pieces are joined into another piece of chalk (4/4=1). So the teacher gets 21 (16+4+1) days out of the 16 pieces of chalk
Rap
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Airhed13
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Re: Brain Teasers and Algebra Riddles
« Reply #6 on: Jul 22nd, 2005, 1:10pm » |
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6. Mr.Brown has 6 black gloves and 8 brown gloves in his closet. He blindy picks up some gloves from the closet. What is the minimum number of gloves Mr. Brown will have to pick up to be certain to find a pair of gloves of the same color?
| hidden: | | If we were talking about socks, the answer'd be three. My typical left-handed glove doesn't fit on my right hand, though, nor does my typical right-handed glove fit on my left hand. With this in mind, and assuming that 6 black gloves and 8 brown gloves means 3 black pairs and 4 brown pairs, the answer is 8 gloves. He could draw 4 brown lefties, 3 black lefties, and then the 8th glove would be either a brown or black rightie. |
Of course, I think the real question is what Mr. Brown is doing with so many pairs of identical gloves. Did the local hardware store have a sale?
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rmsgrey
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Re: Brain Teasers and Algebra Riddles
« Reply #7 on: Jul 23rd, 2005, 10:09am » |
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Whether gloves have handedness usually depends on whether they can be turned inside out or not. Typical latex gloves (as seen on CSI) can be inverted and worn on the other hand.
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Michael Dagg
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Re: Brain Teasers and Algebra Riddles
« Reply #8 on: Jul 23rd, 2005, 11:15am » |
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I know that some surgical gloves can be worn either way.
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Michael Dagg
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Airhed13
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Re: Brain Teasers and Algebra Riddles
« Reply #9 on: Jul 25th, 2005, 5:26am » |
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Yep, some gloves can be worn either way. I've never seen nor heard of a pair of brown surgical gloves, but it's a fair case to make.
I think that it all still boils down to the assumption that the gloves have a certain handedness, though. If they're invertible, then a simple case case could be made for those particular gloves not having handedness. Living in the colder north, I have a great deal more exposure to winter gloves or leather gloves with a proper water barrier than with latex gloves, and winter/leather gloves are generally not invertible. Based on the lack of additional information about Mr. Brown, and the brown and black colorings, I admit that I was envisioning a scenario involving non-invertible leather gloves.
Then again, this question really doesn't even warrant the amount of time I've already spent typing this reply.  There are bigger, more interesting, fish to fry.
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