random brain teasers

[Guest]

Heres some brainteasers for fun

1. A man called John staggers out of a bar and says, “Boy, I’ve had way too many! I’m seeing pink fluffy dinosaurs!” Johns friend laughs and asks “How many drinks DID you have?” John replies I drank a total of 148 ounces. How many of the 22 drinks were 8-ounces and how many were 6-ounces

2. Fill in the blank: Tom’s father has three sons: Larry, Moe, and ________.

3. A man arranges to get $100 and a rare album of polka music for his work at at an office for the first year. After 7 months he leaves the company, and receives the album and $20 for his work. How much is the album worth

4. If the only sister of your mother's only brother has an only child, what would be your relationship to that child?

5. A train goes a mile in 3 minutes with the wind and goes back in 4 minutes going against the wind. Assume that the train’s engine gives the same push to the wheels and the wind is the only reason the train slows down or speeds up (No hills or anything like that. The train goes at a constant speed). The next day, the train does the same mile, but there’s no wind at all. How long does it take?

6. A man is driving down the one-lane street and slams on the brakes when she sees a crazy hobo mooning the city. Unfortunately, there’s a chain reaction as the 9 cars behind slam into her in a single line of angry dented cars. How many bumpers were hit?

Please show reasoning

[Guest]

1.) 8-8oz. & 14-6oz.

X+Y = 22

8X+6Y=148

Solve for X & Y

2.) Tom

3.) Album is $92

12 / (100 + X) = 7 / (20 + X)

Solve for X

4.) Me

5.) 3.42min

1 mi/3min = 20 mph

1 mi/4min = 15 mph

avg = 17.5mph

6.) Assuming the "man" in the question is a typo and supposed to be "woman", the number of bumpers hit is 18

([car9])([car8])([car7])([car6])([car5])([car4])([car3])([car2])([car1])([WOMAN])

[Guest]

Heres some brainteasers for fun

1. A man called John staggers out of a bar and says, “Boy, I’ve had way too many! I’m seeing pink fluffy dinosaurs!” Johns friend laughs and asks “How many drinks DID you have?” John replies I drank a total of 148 ounces. How many of the 22 drinks were 8-ounces and how many were 6-ounces

22 6-oz drinks make 132 ounces. 148 is 16 more than 132, so there had to be 16 extra ounces provided with the 8-ounce drinks. Since each 8-ounce drink provides two more ounces than the 6-ounce drinks, John must have had eight 8-oz. drinks and 14 6-oz. drinks.

2. Fill in the blank: Tom’s father has three sons: Larry, Moe, and ________.

Tom. (Curly was a cousin.)

3. A man arranges to get $100 and a rare album of polka music for his work at at an office for the first year. After 7 months he leaves the company, and receives the album and $20 for his work. How much is the album worth

Straightforward algebra problem. Total compensation for the job is $100 + x, where x is the value of the polka album. Partial compensation, which is 7/12 of total compensation, is $20 + x. Therefore,

(7/12)(100 + x) = 20 + x

Solving for x gives an album value of $92.

4. If the only sister of your mother's only brother has an only child, what would be your relationship to that child?

If my mother's only brother has an only sister, then clearly that must be my mother. Therefore, her only child would be me. The relationship is one of self.

5. A train goes a mile in 3 minutes with the wind and goes back in 4 minutes going against the wind. Assume that the train’s engine gives the same push to the wheels and the wind is the only reason the train slows down or speeds up (No hills or anything like that. The train goes at a constant speed). The next day, the train does the same mile, but there’s no wind at all. How long does it take?

As a physics problem, this is not straightforward, since friction in general (including drag) is approximately proportional to velocity. Thus, the wind "does more damage" going against the train than it benefits the train going the other way.

Nevertheless, the intent of the problem is clear, so let's just solve it that way. The problem seems to want to say that the wind subtracts some velocity v when the train goes into the wind, and adds that same velocity v when the train goes with the wind. If the train's velocity without wind is V, then the velocity into the wind is V - v, and with the wind is V + v.

Using d = rt and solving for r, we see that r = d / t. So

V + v = (1 mile) / (3 minutes)

V - v = (1 mile) / (4 minutes)

Adding these equations, we get

V + v + V - v = (1 mile) / (3 minutes) + (1 mile) / (4 minutes)

2 * V = (4 miles) / (12 minutes) + (3 miles) / (12 minutes)

V = 0.5 * (7 miles) / (12 minutes)

Solving d = rt for t gives t = d / r, so

t = (1 mile) / (0.5 * 7 miles) / (12 minutes))

= (1 mile) * (12 minutes) * 2 / (7 miles)

= 24/7 minutes

= 3 3/7 minutes = about 3 minutes 26 seconds.

6. A man is driving down the one-lane street and slams on the brakes when she sees a crazy hobo mooning the city. Unfortunately, there’s a chain reaction as the 9 cars behind slam into her in a single line of angry dented cars. How many bumpers were hit?

18 bumpers. Total of ten cars in the accident (original car + 9 cars following) gives a total of 20 bumpers, but the front bumper of the front car and the rear bumper of the back car are (we assume) undamaged. (By the way, the antecedent to "her" is "man"...might want to correct that.) (Edited to add the parenthetical statement) (Edited again to add the missing parenthesis...oops)

[bonanova]

1. 8x + 6[22-x] = 148. x=8. => 8 8-oz drinks and 14 6-oz drinks. For 148 oz, John reasoned pretty well.

2. Tom

3. A+$100 = 12m; A+$20 = 7m. => $80 = 5m => m=$16 => A = $92.

4. Me.

5. Train's speed T is changed S by the wind. T+S = 20mph; T-S = 15mph. => T = 17.5mph. It takes 60/17.5 = 3.4286... minutes.

6. You called a man "her". Regardless, 10 cars meet in 9 places. 2 bumpers each => 18 bumpers.

[Guest]

1.

14 x 6-ounces = 84 ounces

8 x 8-ounces = 64 ounces

14 + 8 = 22 drinks

84 + 64 = 148 ounces

2.

Tom. One of the sons of "Tom's father" is obviously Tom.

3.

The remaining 5 months would have give him $80 more so..

1 month = $80 / 5 = $16

7 months = $16 x 7 = $112

Album worth = $112 - $20 = $92

4.

That child would be myself. My mother has a brother and she's his only sister.

5.

Assuming the wind is strong enough to really speed up and slow down the train, it would always take 7 minutes regardless of the wind because the time you earn with the wind, you lose it against the wind.

6.

First, I guess you mean "A woman" because you're using "she" and "her" later.

The 9 cars behind her each hit one bumper so that makes 9 bumpers hit. But if you include bumpers that hit those bumpers, you have a total of 18 bumpers. So there are 10 cars in this accident with all bumpers hit except for the first front and the last rear bumpers.

[bonanova]

5.

Assuming the wind is strong enough to really speed up and slow down the train, it would always take 7 minutes regardless of the wind because the time you earn with the wind, you lose it against the wind.

A better assumption is that the speed you also lose. That leads to a different answer.

5. A train goes a mile in 3 minutes with the wind and goes back in 4 minutes going against the wind. Assume that the train’s engine gives the same push to the wheels and the wind is the only reason the train slows down or speeds up (No hills or anything like that. The train goes at a constant speed). The next day, the train does the same mile, but there’s no wind at all. How long does it take?

The train doesn't go at a constant speed.

[Guest]

Well, these are mostly just simple algebra problems (takes me back a few years), but I tried to do them all in my head. Ended up having to use pen and paper for #3 and #5.

1. 8 eight ouncers and 14 sixers.

x= # of eight oz

y = # of six oz.

y = 22 -x ... 8x + 6y=148 ... (substitute) 8x + 132 - 6x = 148 ... x = 8

2. Tom

3. $92

p = album price

m = month's wage

100 + p = 12m ... 7m = p +20 ... (substitute) 100 + p = 12(p + 20)/7 ... p = 92

4. Me

5. 3 3/7 min

s = speed of train (mile/min)

w = speed added/subtracted by wind

3(s + w) = 4(s - w) ... w=s/7 ... 3min (s+w) = 1 mile ... (substitute) ... 3s + 3s/7 = 1 ... s = 7/24 which means 24/7 mins/mile.

6. 18 (two bumpers for all cars in middle, one each for cars at front and back)

Edited January 24, 2008 by Duh Puck

[Guest]

3: The album's value is independent of the amount of time that the man worked. Considering that it is a polka album, the value is rather low.