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| Acmlm's Board - I3 Archive - Brain Teasers - Math riddles. |
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ziratha Koopa                   Since: 11-19-05 Last post: 6320 days Last view: 6302 days |
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| My dad brought home a book of math type riddles from his work, so I have decided to pass them on to you. I will post 3 at a time, and they will have a point value assigned(most commonly 1 pt) I will keep track of points and such. Let's do it:
#1 = 1 Pt A man went into a bank to cash a check. In handing over the money the casier, by mistake , gave him dollars for cents and cents for dollars. He pocketed the money without examining it, and spent a nickel on his way home. He then found that he possessed exactly twice the amount of the check. He had no money in his pocket before going to the bank. What was the exact amount of the check? #2 = 1pt Three chickens and one duck sold for as much as two geese: one chicken, two ducks, and three geese were sold together for $25.00. What was the price of each bird in an exact number of dollars? #3 = 1pt If an army fourty miles long advances fourty miles while a dispatch rider gallops from the rear to the front, delivers a dispatch to the commanding general, and returns to the rear, how far has he travelled? |
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Alastor Fearless Moderator Hero   Since: 11-17-05 From: An apartment by DigiPen, Redmond, Washington Last post: 6302 days Last view: 6302 days |
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| I don't have a lot of time, so I'm just going to solve the easiest one and go, and the easiest one is #2. Geese are $6, ducks are $3, and chickens are $1. (edited by Alastor the Stylish on 04-28-06 10:39 PM) (edited by Alastor the Stylish on 04-28-06 10:41 PM) |
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Ramon Bullet Bill Since: 11-25-05 Last post: 6302 days Last view: 6302 days |
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| Geese are 5$, ducks are 4$ and chickens are 2$. | |||
NSNick Gohma IF ALL ELSE FAILS USE BOOZE  Since: 11-17-05 From: Last post: 6303 days Last view: 6303 days |
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| 3) 80 miles. | |||
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Alastor Fearless Moderator Hero Since: 11-17-05 From: An apartment by DigiPen, Redmond, Washington Last post: 6302 days Last view: 6302 days |
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| I'm fairly certain that's not the answer, Nick. But it could be; I didn't really understand the question. It seemed more like the answer was more like 90 miles ... But that's just an estimation since I don't feel like bothering with the math. It could work if he was just going there the one way, but he goes back in that time, so.
And Ramon, yeah, I was stupid and misread the question as one goose, not two. This is what happens when you rush. (edited by Alastor the Stylish on 04-29-06 12:59 PM) |
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ziratha Koopa Since: 11-19-05 Last post: 6320 days Last view: 6302 days |
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| We have a winner. Ramon gets one point.
**Note, I will try to demonstrate the solutions myself, even though only the final answers are included in the book. I am good at math so I can probably do most of them** **note the second, If nobody gets these, after a while I will make them bonuses and add 3 new questions..." #2 = solved! Three chickens and one duck sold for as much as two geese: one chicken, two ducks, and three geese were sold together for $25.00. What was the price of each bird in an exact number of dollars? Pure math Solution: Let x = price of chickens, y = price of ducks, and z = price of geese all in dollars. we have that 3x+1y = 2z and that 1x + 2y + 3z = 25 So, x = 25-3z-2y Therefore 3(25-3z-2y) +1y = 2z (substitution) 75 - 9z - 6y +1y = 2z 75 = 11z + 5y We also know that no bird is less than 1 dollar and no more than 20 and are an integer(no decimal) number of dollars. If you look carefully at that last equation, you see that no matter what y is, it will be a multiple of 5. So the only way for 11z + some multiple of 5 to add up to 75 is for 11z to also be a multiple of 5. And the only way for 11z to be a multiple of 5 and be less then 75 and greater than 0 is z = 5. So, geese are $5.00 Now we plug this in. 3x + 1y = 10 y = 10 - 3x since x and y have to be integers, Y can be no smaller than 1 and no bigger than 7. x can be no smaller than 1 and no bigger than 3. If x is one, then y = 10 - 3 = 7, if x = 2 then y = 10 - 6 = 4, if x = 3 then y = 10 - 9 = 1. Plug in the values (1,7,5) , (2,4,5), (3,1,5) for (x,y,z) into 1x + 2y + 3z = 25. 1(1) + 2(7) + 3(5) = 1 + 14 + 15 = 30 which is not 25. 1(2) + 2(4) + 3(5) = 2 + 8 + 15 = 25. So chickens cost $2.00 and ducks cost $4.00 **Note, you could have guessed the answer without the algrebra, but if you are interested, there it is /\** #1 = 1 Pt A man went into a bank to cash a check. In handing over the money the casier, by mistake , gave him dollars for cents and cents for dollars. He pocketed the money without examining it, and spent a nickel on his way home. He then found that he possessed exactly twice the amount of the check. He had no money in his pocket before going to the bank. What was the exact amount of the check? #3 = 1pt If an army fourty miles long advances fourty miles while a dispatch rider gallops from the rear to the front, delivers a dispatch to the commanding general, and returns to the rear, how far has he travelled? #4 = 1pt Can you find values for p and q so that p^q - q^p =1927? By this I mean p raised to the power of q minus q raised to the power of p equals 1927. An example for 1844 is included. 3^7 - 7^3 = 2187 - 343 = 1844 Points: Ramon 1 The rest of you, keep guessing, Just a hint, the answer to #3 is not a rational (able to be exp (edited by ziratha on 04-29-06 06:08 PM) |
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Alastor Fearless Moderator Hero Since: 11-17-05 From: An apartment by DigiPen, Redmond, Washington Last post: 6302 days Last view: 6302 days |
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I rather suspected as much 
Gods, I haven't done algebra in so long... But #4 is easy. p=2, q=11. |
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ziratha Koopa Since: 11-19-05 Last post: 6320 days Last view: 6302 days |
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| Hey, that's right. I won't show the solution since you can just toss that into a calculator solver function. Plus I don't know how to post radical signs and such on the board (aka me = lazy).
#4 = solved by alastor Can you find values for p and q so that p^q - q^p =1927? By this I mean p raised to the power of q minus q raised to the power of p equals 1927. An example for 1844 is included. 3^7 - 7^3 = 2187 - 343 = 1844 Solution: p = 2 , q = 11. #1 = 1 Pt A man went into a bank to cash a check. In handing over the money the casier, by mistake , gave him dollars for cents and cents for dollars. He pocketed the money without examining it, and spent a nickel on his way home. He then found that he possessed exactly twice the amount of the check. He had no money in his pocket before going to the bank. What was the exact amount of the check? #3 = 1pt If an army fourty miles long advances fourty miles while a dispatch rider gallops from the rear to the front, delivers a dispatch to the commanding general, and returns to the rear, how far has he travelled? #5 = 2pt The discussion arose before one of the tribunals as to which of a tradesman's sons could best be spared for service in the army. "All I know as to their capacities," said the father, "is this: Arthur and Benjamin can do a certain quantity of work in eight days, which Arthur and Charles will do in nine days, and which Benjamin and Charles will take 10 days total.' At which point it was apparant that Charles was the slowest worker and would be drafted. However, it was wondered: What amount of time is required for each of the sons working alone? Points: Ramon 1 Alastor the Stylish 1 (edited by ziratha on 04-29-06 08:37 PM) |
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Skreename Giant Red Paratroopa Since: 11-18-05 Last post: 6308 days Last view: 6302 days |
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| 3: $31.63.
5: Arthur would take 14 days, Benjamin would take 18 days, Charles would take 22 days. Assuming I did that right... Otherwise, it may need to be halved. |
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ziratha Koopa Since: 11-19-05 Last post: 6320 days Last view: 6302 days |
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| ME say you meant # 1. not 3. But that is a correct answer, so: +1 there. As for the three bros, technically they are fractions, not whole numbers in this question, so... humm i'll give you this one, but in the future I WANT PRECISE ANSWERS. (I'm allowing this one because the answers are withing rounding range so you may have gotten the precise answers and just rounded... The one answer for the riddle involving the army was not so close) If the problem doesn't say it's whole numbers, then fractions are allowed. In the future, if the problem is not precise, then you may not get the whole value of the riddle. sorry.
Points: Skreename 3 points <-first place! Ramon 1 Alastor the Stylish 1 #1 = solved by skreenname A man went into a bank to cash a check. In handing over the money the casier, by mistake , gave him dollars for cents and cents for dollars. He pocketed the money without examining it, and spent a nickel on his way home. He then found that he possessed exactly twice the amount of the check. He had no money in his pocket before going to the bank. What was the exact amount of the check? Reading carefully we can get the following equation: 2*(100*A + B) = 100B + A - 5 Where A is the dollars of the check and B is the cents. 199A=98B-5 Solving for A A=(98B-5)/199 Place it in a simple y=mx +b type format and plug into the calc to find whole numbers. You need whole numbers in this one because you can't have a fractional cent and a fractional dollar is cents, so... we get: 31.63 #5 = solved by skreenname The discussion arose before one of the tribunals as to which of a tradesman's sons could best be spared for service in the army. "All I know as to their capacities," said the father, "is this: Arthur and Benjamin can do a certain quantity of work in eight days, which Arthur and Charles will do in nine days, and which Benjamin and Charles will take 10 days total.' At which point it was apparant that Charles was the slowest worker and would be drafted. However, it was wondered: What amount of time is required for each of the sons working alone? answer: a/b equals speed of arthur, c/d = speed of benjamin and e/f = speed of charles. We know that 8*(a/b + c/d) = 1 (the quantity of work is unimportant so this is one) and that 9*(a/b + e/f) = 1 and that 10*(c/d + e/f) = 1. so: a/b + c/d = 1/8 and a/b = 1/8 - c/d a/b + e/f = 1/9 and (1/8 - c/d) + e/f = 1/9 e/f = 1/9 - 1/8 + c/d c/d + e/f = 1/10 c/d + 1/9 - 1/8 + c/ d = 1/10 2c/d = 1/10 - 1/9 + 1/8 = 9/90 - 10/90 + 1/8 = -1/90 + 1/8 The lcm of 90 and 8 is 360, so...: 2c/d=-4/360 + 45/360 = 41/360, divide by the '2' makes it 41/720 = speed of benjamin. So, We have that 1 = T * 41/720 where T is the time. so, T = 720/41 = 17 and 23/41 days to finsih by himself. Now we can plug the information back into the equations to find the other bros' speeds and times. a/b + c/d = 1/8 as you recall, so: a/b + 41/720 = 1/8 a/b = 1/8 - 41/720 a/b = 90/720 - 41/720 = 49/720 So, we nned his time. again, we can get this by: 1 = T * a/b 1 = T * 49/720 T = 720 / 49 days. = 14 and 34/49 days to complete. = arthur's time. c/d + e/f = 1/10, so 41/720 + e/f = 1/10 e/f = 72/720 - 41/720 = 31/720 1 = T * e/f 1 = T * 31/720 T = 720/31 = 23 and 7/31 days. So all told, Arthur would take 14 and 34/49 days, Benjamin would take 17 and 23/41 days, and charles would take a laughable 23 and 7/31 days. #3 = 2pts If an army fourty miles long advances fourty miles while a dispatch rider gallops from the rear to the front, delivers a dispatch to the commanding general, and returns to the rear, how far has he travelled? Time for a visual puzzle: #6 = 1 pt Once upon a tine there were nine prisoners of particularly dangerous character who had to be carefully watched. Every day but sundays they were taken out for exercise, handcuffed together, as shown in the diagram made by a guard. On no day in any one week were the same two men to be handcuffed together. On monday they were sent out handcuffed as shown below. Can you arrange the nine men in triplets for the remaining 5 days. Obviously #1 cannot be next to #2 on either side, and # 2 cannot be next to either #1 or #3 on either side etc. 1~2~3 4~5~6 7~8~9 So assuming they are innitially arranged as above, arrange them into 5 more groups of 3 so that no 2 men are side by side in any two of the six groupings. #7 = 1pt What is the smallest triangle who's side's are lengths of consecutive integers and who'se area is exaclty divisible by 20? *note, I am going to add one point to the value of #3.* *note the second, From now on, all riddles will start with one point and if they go unsolved for a day or two I will add more points.* (edited by ziratha on 05-01-06 10:09 PM) |
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Kejardon Shyguy  Since: 05-21-06 Last post: 6303 days Last view: 6302 days |
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| hmm. I think I'll tackle #3, seeing as nobody else is.
Currently, it's unclear when the army has moved 40 miles: Is this the time it takes the rider to go from rear to front? Or is it the time it takes the rider to go from rear to front to rear? Assuming the first, this means that the rider is moving at twice the speed of the army. When returning, he will move through the army at a relative rate of 3 times as quickly as when he moved to the front of the army. This means 4/3 the time it takes the army to move 40 miles, at a rate of twice the army's speed, or 8/3 of 40 miles, or 320/3 miles. You said it's not rational though, so that's obviously not the right answer. So, the army moves 40 miles in the time it takes the rider to travel to the front and return to the rear. The rider moves 40 miles inherently because the army moved 40 miles. Then he made a round trip for the last part: The distance the army moved while the rider traveled to reach the front. The total distance is thus 40 + 2 * distance1. In the same time the army moves distance1, the rider moves 40 + distance1. Also, in the time the army moves 40 - distance1, the riders moves distance1. Divide the two equations and you get distance1 / (40 - distance1) = (40 + distance1) / distance1, or 2 * distance1 ^ 2 = 1600. Distance1 is thus 20 * sqrt(2) The total distance is then easily calculated as 40 (1 + sqrt (2)), or roughly 96.569 miles. |
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ziratha Koopa Since: 11-19-05 Last post: 6320 days Last view: 6302 days |
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| That's a big 10 four! The second answer is correct. 2 points to you. I fear that nobody else is going to post, but I will keep posting riddles so long as there are players.
Points: Skreename 3 points <-first place! Kejardon 2 Ramon 1 Alastor the Stylish 1 #3 = solved by kejardon If an army fourty miles long advances fourty miles while a dispatch rider gallops from the rear to the front, delivers a dispatch to the commanding general, and returns to the rear, how far has he travelled? Time for a visual puzzle: #6 = 1 pt Once upon a tine there were nine prisoners of particularly dangerous character who had to be carefully watched. Every day but sundays they were taken out for exercise, handcuffed together, as shown in the diagram made by a guard. On no day in any one week were the same two men to be handcuffed together. On monday they were sent out handcuffed as shown below. Can you arrange the nine men in triplets for the remaining 5 days. Obviously #1 cannot be next to #2 on either side, and # 2 cannot be next to either #1 or #3 on either side etc. 1~2~3 4~5~6 7~8~9 So assuming they are innitially arranged as above, arrange them into 5 more sets of groups of 3 so that no 2 men are side by side in any two of the six groupings. #7 = 2pt What is the smallest triangle who's side's are lengths of consecutive integers and who'se area is exaclty divisible by 20? #8 = 1 pt. It is found that 32,547,891 multiplied by six (thus using all the nine digits once and once only) gives the product 195,287,346 (also containing the nine digits, and only once). Can you find another number to be multiplied by six under the same condition? that it, the 9 digits are all in the initial number, and the product of that number and 6, and the nine digits only appear once each. #9 = 1pt A grocer proposed to put up 20 lbs. of china tea into 2-lb packets, but his weights had been misplaced by somebody, and ge could only find the 5-lb and the 9-lb. weights. What is the quickest way for him to do the business? We will say at once that only nine weighings are really necessary. (edited by ziratha on 05-26-06 08:22 PM) |
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Schweiz oder etwas [12:55] (Dr_Death16); I swear, the word drama needs to be stricken from the dictionary, for I've heard it so many times, it will permanently be imprinted on my brain  Since: 11-17-05 From: Kingston, Rhode Island Last post: 6302 days Last view: 6302 days |
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| #9: First, weigh out five pounds.
Put that on the nine pound weight. Weigh out another five pounds. Add what you have to the nine pound weight, what is left is one. Put that in a bag. Repeat once. That puts you up to eight steps. The ninth weighing is the one where you put the two pound bag that you've discovered on some kind of counterbalance. You have a single two pound bag. From here, you can use that two pound bag as a reference point for the rest of the bags, and you don't even need to weigh them numerically, you just have to make sure they're all equal in weight to the first one. (edited by Xyger on 05-27-06 09:53 AM) |
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ziratha Koopa Since: 11-19-05 Last post: 6320 days Last view: 6302 days |
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| Sorry, that is incorrect. You only need 9 weighings to have all the tea in 2 lb bags, not one 2 lb bag to compare with. Also, +1 point to the puzzles values... | |||
Teundusia Red Cheep-cheep Since: 11-18-05 Last post: 6304 days Last view: 6310 days |
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| 7. A triangle that has lengths of 3, 4 and 5 down each of its sides? | |||
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Alastor Fearless Moderator Hero Since: 11-17-05 From: An apartment by DigiPen, Redmond, Washington Last post: 6302 days Last view: 6302 days |
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| I'm fairly certain 6 isn't divisible by 20. | |||
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ziratha Koopa Since: 11-19-05 Last post: 6320 days Last view: 6302 days |
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| insert approptriate stunning response here*..
ooh, beat me to the punch alastor! |
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