Here are three versions of the River Crossing problem. Be the first to solve any one of the three versions to win a prize.
Version 1:
A farmer is traveling with a lion, a sheep, and a basket of cabbages. He comes to a river and finds a small boat that holds only himself and one passenger. For obvious reasons, he can't leave the lion alone with the sheep, or the sheep with the cabbages. How does he get his cargo safely to the other side?
Version 2:
Two couples need to go across a river. They find a small boat that holds only two passengers at a time. Each jealous husband would not allow his wife to be with the other husband anywhere unless he is also present. How can they cross the river?
Version 3:
Same as version 2, but with three couples.
(Due Friday, January 11, 2008)
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22 comments:
Version 1:
Step 1: he takes the sheep w/ him
Step 2: he goes back and gets the lion and takes the sheep back w/ him. He picks up the cabbages and drops off the sheep. He drops of the cabbages on the other side and goes back to get the sheep.
Version 2:
Step 1: the two wives go
Step 2: 1 wife goes back and gets her husband
Step 3: the couple gets off so that the other wife could go get her husband.
- Kelvin Rodriguez
Version 1:
The farmer should put the sheep across the river first, then come back and take the cabbage, then bring back the sheep and take the lion to the other side where the cabbage is then go back, get the sheep, and get it to the side where the lion and the cabbage are.
Version 2:
Let 1 man take his wife to the other side then he can go back pick up the other man, when they both get to the other side, first man is going to stay with his wife and let the other man go back to pick up his wife.
Version 2:
One husband crosses the river with his wife. That husband comes back and picks up the other husband. The first husband goes with his wife and the second husband goes back for his wife. Then they are across.
Version 2:
Both husbands go across the river first, then husband 1 goes and gets his wife, wife 1 then go back across the river. Husband 1 gests off and wife 1 gets wife 2 across the river.
Version 1:
He takes the sheep first, and then goes back to the other side and picks up the cabbage and takes it to the sheep and picks up the sheep and leaves the cabbage. Then goes back to the other side with the sheep and picks up the lion and leaves the sheep. The farmer goes across again and drops off the lion and leaves it with the cabbage. He goes across again and picks up the sheep and goes back. And he is done.
Version 2:
The 2 husbands go first. One stays on the other side. The husband that stays on the boat goes and picks up his wife and goes across again. The couple stays on that side. The other husband goes across to pick up his wife, and that couple goes across and then it is done.
I think we have the first two versions solved. Who has a correct solution? To win the remaining prize, you will need to solve the third version. For convenience, you can call the couples A&a, B&b, and C&c.
version 3:
1- the wife from the first couple takes the wife from the third couple to the other side.
2- the wife from the first couple goes back.
3- the husband of the first couple takes the husband of the third couple to the other side to stay with his own wife.
4- the husband from the first couple goes back.
5- the wife of the second couple takes her husband to the other side.
6- the wife of the second couple goes back.
7- the wife of the first couple takes the wife of the second couple to the other side.
8- the wife of the second husband goes back to ether husband and take him to the other side.
-Katherine Fernandez
Comments on Katherine Fernandez's solution:
After step 3, you have the second couple on one side with the wife of the first couple. This is not allowed because the first wife is with the second husband while her husband is not around.
Version 1
Trip 1: Take the sheep over and come back with nothing.
Trip 2: Take the lion over and come back with the sheep.
Trip 3: Take the cabbages over and come back with nothing.
Trip 4: Take the sheep over.
Version 1:
First the man takes the sheep, leaves it, then goes to pick up the cabbage, leaves it, then takes the sheep back and leaves it, picks up the lion and leaves it, then goes back to pick up the sheep.
Version 2:
1 couple crosses then the husband goes back to pick up the other husband then goes back to pick up his wife.
Version 3:
1 couple crosses then her husband goes back to pick up the other husband then he goes back to pick up his wife. Then her husband goes back and picks up the other man then he goes back to pick up his wife.
Version 1:
Let F = farmer, L = lion, S = sheet, C = cabbage
FLSC |
LC | FS
LCF | S
L | CFS
LFS | C
S | LFC
FS | LC
| FSLC
Version 2:
Let M1 = husband #1
W1 = wife #1
M2 = husband #2
W2 = wife #2
M1 W1 M2 W2 |
M1 W1 | M2 W2
M1 W1 M2 | W2
W1 | M1 M2 W2
W1 M1 | M2 W2
| M1 W1 M2 W2
To get across the river safely, there will have to be many trips made. First, one couple go, then the husband of that couple comes back while his wife is on the other side. Then he stays alone and let the couple that stayed go. He then leaves his wife there and he comes back alone. Now there are only 2 guys that need to get across, so they go. Now everyone is on the other side.
i thought you would say that! =[
i thought since he was also with his own wife he wouldn't care,
anyways i thought it over... here goes another try!!!
version 3-
1. the wife from the third couple takes the wife from the first couple to the other side.
2.the wife from the third couple goes back.
3. the husband from the third couple takes the wife from the third couple to the other side.
3. the husband from the third couple goes back.
4. the husband from the second couple takes the wife from the second couple to the other side.
5. the husband from the second couple goes back.
6. the husbands from the first and second couples go to the other side.
7. the wife from the third couple goes back.
8. The husband and wife from the third couple go to the other side.
-Katherine Fernandez =]
Response to Katherine's second solution:
After step 3, the wife from the first couple is on the same side with husband and wife from the third couple while her husband is on the other side. Not good!
w/e newaysz a new 1:
1. wife one and husband one go across
2. wife one goes back and picks up wife two
3. wife two takes wife one to the other side
4. wife two goes back and gets husband two
5. wife two and husband two go across
6. wife two goes back to get wife three
7. wife three goes to take wife two across
8. wife three goes back
9. wife three and husband three go across
the second time i sent you the answer to version 3 was right i find nothing wrong with it. read it over to explain to me why it is wrong thx
Katherine, here’s the problem with your version 2:
Let’s use the notation Aa, Bb, Cc to represent the three couples where A, B, and C are the husbands and a, b, and c are the wives. Let’s use the vertical line “|” as the river to divide the two sides. Your second solution looks like this –
1. the wife from the third couple takes the wife from the first couple to the other side.
2.the wife from the third couple goes back.
3. the husband from the third couple takes the wife from the third couple to the other side.
0. AaBbCc|
1. ABbC|ac
2. ABbCc|a
3. ABb|aCc
At this point, notice that wife a is on the right-hand-side with husband C while her husband, A, is on the other side. This is not allowed. Also, let me point out that wife b is on the left-hand-side with husband A, but this is okay since her husband, B, is also there with her.
Your third solution looks like this:
1. wife one and husband one go across
2. wife one goes back and picks up wife two
0. AaBbCc|
1. BbCc|Aa
2. BbCca|A
Again, at this point, wife a is on the left-hand-side with two other husbands (B and C) while her husband is on the other side. This is also not allowed.
Keep trying! I am glad to see that you have not given up.
VERSION 3:
1.the couples go to couple therapy
2.the therapist tells the husbands to stop being so over protective
3.the husbands listen
4.they go back to the river
5.they all go in any order not worrying about who is with who
6.everyone is over, no one died, everyone is safe
7.the couples live happily ever after
8.ms.hsiao gives Katherine $10 for solving the problem
9.ms.hsiao also passes Katherine for the marking period =]
ms.hsiao,
what happens if no one answers the question to version 3? do u give the money to no one or the person that got the closest to the answer or the only person that tried???
VERSION 3:
1. husband 1 takes wife 1 to the other side
2. husband 1 goes back
3. wife 3 takes wife 2 to the other side
4. wife 3 goes back
5. husband 2 takes husband 1 to the other side
6. husband 2 and wife 2 go back
7. husband 2 and husband 3 go to the other side
8. wife 1 goes back
9. wife 2 and 3 go to the other side
10. wife 2 goes back
11. wife 1 and wife 2 go to the other side
HAHAHA!!! flawless =P
Prizes are awarded only for correct answers. Does Katherine have it?
Version 1:
First the framer moves the sheep to the other side, leaving the cabbages and the lion. Then he goes to get the lion and brings it to the side where the sheep is. Then he moves the sheep back to the side where the cabbages are, leaving the lion alone. Then he leaves the sheep and takes the cabbages to the side where the lion is and then comes back to get the sheep and take it across the river. Now he has successfully moved the cargo across the river.
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