Brain Teasers
Park It Ranger
Ranger Cadet Bu Star has just been given the task of moving the five cases of Park Pop soda at the Weiss Pavilion to the Wirth Pavilion, which is 5 miles away. For transportation, Bu must use a MoJoPed, a moped which runs on Park Pop. It can carry, at most, its rider and 25 bottles of soda, i.e., one case in its cargo carrier and one bottle in its fuel tank. It gets one mile to the bottle and is currently empty; it will only move under Pop power. How many unopened bottles can Bu deliver to the second pavilion?
Comments to triflers:
The bottles and cases are hi-tech, so there are no concerns about theft or littering. They can stay parked or be discarded anywhere. Yes, the constant rate of fuel use is unreal, and yes, of course, I am asking for the maximum number of bottles!
Comments to triflers:
The bottles and cases are hi-tech, so there are no concerns about theft or littering. They can stay parked or be discarded anywhere. Yes, the constant rate of fuel use is unreal, and yes, of course, I am asking for the maximum number of bottles!
Hint
There are hints in the comments to triflers and in the title.Answer
80To achieve this surprising result, Bu must first take the five cases, one at a time, and park them at a point along the route 2 5/18 miles from the Weiss Pavilion. This takes 9 trips of 2 5/18 miles (5 advancing trips interspersed with 4 return trips) for a total of 20.5 miles traveled (9 * 2 5/18 = 20.5) and 20.5 bottles of soda used. Cadet Star now has 99.5 bottles of soda. (5 * 24 - 20.5 = 120 - 20.5 = 99.5) He puts 3.5 of these aside and redistributes the other 96 to completely fill four cases. With one less case to move, Bu will now make 2 fewer trips. The 3.5 bottles set aside are used to move the four cases the next 1/2 mile toward the Wirth Pavilion. After this, the Wirth Pavilion is just 2 2/9 miles away ( 5 - 2 5/18 - 9/18 = 2 4/18 ). Next, he travels 15 5/9 miles (7 * 2 2/9) using 15 5/9 bottles of soda to complete his trip. The ranger cadet delivers 80 bottles to the pavilion and has 4/9 of a Park Pop to spare. (96 - 15 5/9 = 80 4/9)
Hide Hint Show Hint Hide Answer Show Answer
What Next?
View a Similar Brain Teaser...
If you become a registered user you can vote on this brain teaser, keep track of which ones you have seen, and even make your own.
Solve a Puzzle
Comments
Yes, this teaser does resemble - Camel and Watermelons. It is very different in that the legacy teaser made it very apparent special action was needed. The legacy is also wrong because the accepted answer is wrong by two watermelons.
Dec 25, 2006
i thot 80 bottles wud be a more efficient answer...?? wat do ya think...
take the case 0f 25 plus one bottle frm the fifth case fr d fuel..fr the trip he'll consume 9 bottles frm the case hes transporting..so leaving 16 at d destination...likewise 16*4=64 bottles frm his first 4 trips....then hes left with 25-1*4=21 bottles at d source...he'll consume 5 bottles out of the 21...16 left
..count all..64+16=80..?????
take the case 0f 25 plus one bottle frm the fifth case fr d fuel..fr the trip he'll consume 9 bottles frm the case hes transporting..so leaving 16 at d destination...likewise 16*4=64 bottles frm his first 4 trips....then hes left with 25-1*4=21 bottles at d source...he'll consume 5 bottles out of the 21...16 left
..count all..64+16=80..?????
Dec 25, 2006
neways ...he must hav consumed 1/9 th bottle on the eve of christmas....
so my ans matches urs...
merry christmas
so my ans matches urs...
merry christmas
I am not at all certain about newbie's comments. Careful reading of teaser should show that a case is precisely 24 bottles.
Dec 26, 2006
oh..im so srry guys...misunderstood d teaser....proves im a newbie....i take my
comment...
comment...
I hope that he only needs 8/9th of a bottle to drink on his walk back. Good teaser!
I got the same answer doing it differently though... (actually I didn't have 8/9th left so I guess your answer is slightly better but the total unopened bottles is the same)
If you just stop at each mile and leave whatever is left at that point you end up using 9 bottles for the first 3 miles (27) and 7 for the next 2 miles (14) - 120-27-14 = 79...
Make sense?
If you just stop at each mile and leave whatever is left at that point you end up using 9 bottles for the first 3 miles (27) and 7 for the next 2 miles (14) - 120-27-14 = 79...
Make sense?
acobra-
You are quite right. There are many ways to arrive with 79 bottles. One could use the first bottle opened (and each subsequent bottle as it is opened)to move the five cases 1/9 of a mile. One could do as you suggest and use the first bottle to move the first case 1 mile and use the second bottle to return for the others. One could also use the first 3 bottles to move the first case 3 miles and use the next 3 for the return trip.
You are quite right. There are many ways to arrive with 79 bottles. One could use the first bottle opened (and each subsequent bottle as it is opened)to move the five cases 1/9 of a mile. One could do as you suggest and use the first bottle to move the first case 1 mile and use the second bottle to return for the others. One could also use the first 3 bottles to move the first case 3 miles and use the next 3 for the return trip.
Good one.
I too had used the approach of moving the cases a mile at a time.
Nice job
I too had used the approach of moving the cases a mile at a time.
Nice job
that was totally different than my initial approach
I have tried this several times, and I keep getting 80 bottles, not 79. In my scenario, I move the cases in 1/2 mile increments. So, to move four full cases plus the partial case the first 1/2 mile requires nine 1/2 mile trips, or 4.5 bottles, leaving 115.5 bottles. The next half mile leaves me with 111 bottles. After 1.5 miles, I am down to 106.5 bottles. After, 2 miles, 102 bottles. After 2.5 miles, 97.5 bottles. During the next 1/2 mile, I need to start using another case, which means that I now only have to make seven trips, or 3.5 bottles, to move the remaining cases 1/2 mile. So, after 3 total miles, I still have 94 bottles. After 3.5 miles, I have 90.5 bottles. After 4 miles, 87 bottles. After 4.5 miles, 83.5 bottles. After 5 miles, 80 bottles.
cnmne-
Ouch! Congrats!
If my correction goes though, you'll see I've squeezed still more Pop out of the situation.
Thanks and cudos.
Ouch! Congrats!
If my correction goes though, you'll see I've squeezed still more Pop out of the situation.
Thanks and cudos.
Apart from trial and error it would be nice if the proponents of these very interesting answers could explain WHY certain parameters were used. We can understand the arithmetic and see that the given situation delivers 80 bottles but is there some logic that dictates that this answer is the maximum? Am I missing a principle here?
OK. I've checked and rechecked and I can deliver 81 bottles and still have half a bottle in the tank.
I did it similar to cnmne with an important difference. Each trip the park ranger leap frogs, topping off the gas tank at each half mile increment going forward (so as to always be carrying a full tank forward) and then on the return trip he always leaves each 1/2 mile station with only 1/2 bottle in the tank. He always carries the maximum forward and the minimum back.
Where he saves the extra bottle is on his eighth trip because he is able to carry the bottles from two 1/2 mile stations in a single trip. Saving this 1/2 mile round trip saves him a bottle of pop.
The 1/2 mile stations of soda look like the following at the point that the ranger arrives with an empty tank at the farthest back station.
120
95 24
70 23.0 24
45 22.0 23 24
20 21.0 22 23.0 24
00 15.5 21 22.0 23 24
00 00.0 11 21.0 22 23 24
00 00.0 00 06.5 21 22 23.0 24
00 00.0 00 00.0 02 21 22.0 23 24
00 00.0 00 00.0 00 00 19.5 22 23.0 24
00 00.0 00 00.0 00 00 00.0 16 22.0 23 24
00 00.0 00 00.0 00 00 00.0 00 12.5 22 48
00 00.0 00 00.0 00 00 00.0 00 00.0 10 72
00 00.0 00 00.0 00 00 00.0 00 00.0 00 81
By the way, this was my first solution before reading the hint, answer, or comments. I'm fairly certain this is optimal. The total wasted forward capacity (distance * bottles less than 24 in load) is 2.34375 bottles. This gives an absolute limit to the solution (a solution with zero waste) of 81.5 + 2.34 = 83.84 or 83 unopened bottles.
I did it similar to cnmne with an important difference. Each trip the park ranger leap frogs, topping off the gas tank at each half mile increment going forward (so as to always be carrying a full tank forward) and then on the return trip he always leaves each 1/2 mile station with only 1/2 bottle in the tank. He always carries the maximum forward and the minimum back.
Where he saves the extra bottle is on his eighth trip because he is able to carry the bottles from two 1/2 mile stations in a single trip. Saving this 1/2 mile round trip saves him a bottle of pop.
The 1/2 mile stations of soda look like the following at the point that the ranger arrives with an empty tank at the farthest back station.
120
95 24
70 23.0 24
45 22.0 23 24
20 21.0 22 23.0 24
00 15.5 21 22.0 23 24
00 00.0 11 21.0 22 23 24
00 00.0 00 06.5 21 22 23.0 24
00 00.0 00 00.0 02 21 22.0 23 24
00 00.0 00 00.0 00 00 19.5 22 23.0 24
00 00.0 00 00.0 00 00 00.0 16 22.0 23 24
00 00.0 00 00.0 00 00 00.0 00 12.5 22 48
00 00.0 00 00.0 00 00 00.0 00 00.0 10 72
00 00.0 00 00.0 00 00 00.0 00 00.0 00 81
By the way, this was my first solution before reading the hint, answer, or comments. I'm fairly certain this is optimal. The total wasted forward capacity (distance * bottles less than 24 in load) is 2.34375 bottles. This gives an absolute limit to the solution (a solution with zero waste) of 81.5 + 2.34 = 83.84 or 83 unopened bottles.
Stil has pointed out two errors in my solution above that result in only 80 bottles being delivered with an empty tank. The trip that starts with 19.5 bottles starts with only 19 bottles. The half-bottle error propagates forward until the last trip where the second error had 10 bottles. The 10 becomes 8.5 and the number delivered is 80.
Guess I should have checked a third time.
Guess I should have checked a third time.
OK people I will deliver an answer that is slightly better than Stihl's own answer in that I can still deliver 80 bottles but it only takes 2\two shifts not three and I end up with soda pop in my tank! Here goes. (I will also attempt to explain the logic behind the thinking as well as just crunch the numbers)
Firstly I will move the five cases a distance that will use up ALMOST a whole case but I will still have 4 cases to move so I need an extra 4 bottles to power my machine. Thus after my first move I want 4 cases + 4 bottles left = 100 bottles so I must use 20 bottles in 9 trips (4 return trips and one single).
Thus I must make my first dump at 20/9 = 2 2/9 miles from Weiss stadium leaving 2 7/9 miles to go to Wirth stadium. I set aside the 4 bottles for fuel and I do the 7 trips required to move the 4 cases using 7 x 2 7/9 = 19 4/9 bottles. 100 - 19 4/9 = 80 5/9 so I can deliver 80 bottles alright but I have done better than Stihl because I have 5/9 of a bottle left over!
I can explain the strategy of the last 4 case movements. I load a case + 1 bottle for fuel and do 2 7/9 miles finishing with 2/9 of a bottle in my tank. I remove 3 bottles from what's left for the return trip delivering 19 bottles. So I start with 3 2/9 bottles on the return trip of 2 7/9 leaving an excesss of 4/9 of a bottle. When I am 4/9 of a mile from Weiss stadium I drop 4/9 of a bottle (using one of the empties that I have saved) and make it to the stadium exactly empty. I load up with 1 case and 1 bottle and drive 4/9 of a mile using 4/9 of a bottle where I retrieve my cached 4/9 and top up what I have used starting 2 1/3 miles from Wirth with 25 bottles. I arrive and deliver 19 bottles leaving with 3 2/3 bottles - an excess of 8/9 of a bottle. Again when I am 8/9 of a mile from Weiss I drop my 8/9 excess and arrive empty. I load up with 25 bottles, drive 8/9 mile and top up my fuel bottle leaving 8/9 from Weiss with 25 bottles. I use 1 8/9 bottles and deliver 20 this time departing with 3 1/9. I drop my last cache 1/3 mile from Weiss, pick up 25 , top up fuel at 1/3 mile and complete the trip of 2 4/9 miles delivering 22 bottles with 5/9 bottle left!
Firstly I will move the five cases a distance that will use up ALMOST a whole case but I will still have 4 cases to move so I need an extra 4 bottles to power my machine. Thus after my first move I want 4 cases + 4 bottles left = 100 bottles so I must use 20 bottles in 9 trips (4 return trips and one single).
Thus I must make my first dump at 20/9 = 2 2/9 miles from Weiss stadium leaving 2 7/9 miles to go to Wirth stadium. I set aside the 4 bottles for fuel and I do the 7 trips required to move the 4 cases using 7 x 2 7/9 = 19 4/9 bottles. 100 - 19 4/9 = 80 5/9 so I can deliver 80 bottles alright but I have done better than Stihl because I have 5/9 of a bottle left over!
I can explain the strategy of the last 4 case movements. I load a case + 1 bottle for fuel and do 2 7/9 miles finishing with 2/9 of a bottle in my tank. I remove 3 bottles from what's left for the return trip delivering 19 bottles. So I start with 3 2/9 bottles on the return trip of 2 7/9 leaving an excesss of 4/9 of a bottle. When I am 4/9 of a mile from Weiss stadium I drop 4/9 of a bottle (using one of the empties that I have saved) and make it to the stadium exactly empty. I load up with 1 case and 1 bottle and drive 4/9 of a mile using 4/9 of a bottle where I retrieve my cached 4/9 and top up what I have used starting 2 1/3 miles from Wirth with 25 bottles. I arrive and deliver 19 bottles leaving with 3 2/3 bottles - an excess of 8/9 of a bottle. Again when I am 8/9 of a mile from Weiss I drop my 8/9 excess and arrive empty. I load up with 25 bottles, drive 8/9 mile and top up my fuel bottle leaving 8/9 from Weiss with 25 bottles. I use 1 8/9 bottles and deliver 20 this time departing with 3 1/9. I drop my last cache 1/3 mile from Weiss, pick up 25 , top up fuel at 1/3 mile and complete the trip of 2 4/9 miles delivering 22 bottles with 5/9 bottle left!
Except for the generally inferred implication that open bottles are subject to green effect and decompose or are recycled moments after abandonment.
To post a comment, please create an account and sign in.
Follow Braingle!