A morning maths puzzle
Discussion
I am changing careers and am ears deep in a maths text book. The book has questions at the end of each chapter, but gives no workings of the answer.
The question is:
Amy, Jim, John and Kelly are standing on the east bank of a river and wish to cross to the west side using a canoe. The canoe can hold at most two people at a time. Amy, being the most athletic, can row across the river in 1 minute. Jim, John, and Kelly would take 3, 6, and 9 minutes respectively. If two people are in the canoe, the slower person dictates the crossing time. The objective is for all four people to be on the other side of the river in the shortest time possible.
What is the shortest time for moving all four people to the other side of the river?
The shortest time I can get to is 20 minutes. The answer in the book is 19 minutes... discuss!
The question is:
Amy, Jim, John and Kelly are standing on the east bank of a river and wish to cross to the west side using a canoe. The canoe can hold at most two people at a time. Amy, being the most athletic, can row across the river in 1 minute. Jim, John, and Kelly would take 3, 6, and 9 minutes respectively. If two people are in the canoe, the slower person dictates the crossing time. The objective is for all four people to be on the other side of the river in the shortest time possible.
What is the shortest time for moving all four people to the other side of the river?
The shortest time I can get to is 20 minutes. The answer in the book is 19 minutes... discuss!
ILikeCake said:
I am changing careers and am ears deep in a maths text book. The book has questions at the end of each chapter, but gives no workings of the answer.
The question is:
Amy, Jim, John and Kelly are standing on the east bank of a river and wish to cross to the west side using a canoe. The canoe can hold at most two people at a time. Amy, being the most athletic, can row across the river in 1 minute. Jim, John, and Kelly would take 3, 6, and 9 minutes respectively. If two people are in the canoe, the slower person dictates the crossing time. The objective is for all four people to be on the other side of the river in the shortest time possible.
What is the shortest time for moving all four people to the other side of the river?
The shortest time I can get to is 20 minutes. The answer in the book is 19 minutes... discuss!
Have just seen the previous reply, so scrub my answer................The question is:
Amy, Jim, John and Kelly are standing on the east bank of a river and wish to cross to the west side using a canoe. The canoe can hold at most two people at a time. Amy, being the most athletic, can row across the river in 1 minute. Jim, John, and Kelly would take 3, 6, and 9 minutes respectively. If two people are in the canoe, the slower person dictates the crossing time. The objective is for all four people to be on the other side of the river in the shortest time possible.
What is the shortest time for moving all four people to the other side of the river?
The shortest time I can get to is 20 minutes. The answer in the book is 19 minutes... discuss!
Oh, maybe I should put the career change on hold 
Okay if that was too easy how about this:
You are given two identical balls made of a tough alloy. The hardness test fails if a ball dropped from a floor of a 120-storey building is dented upon impact. A ball can be reused in fresh drops only if it has not been dented in a previous drop. Using only these two identical balls, what is the smallest number of ball drops that will determine the highest floor from which the ball can be dropped without being damaged?
Okay if that was too easy how about this:
You are given two identical balls made of a tough alloy. The hardness test fails if a ball dropped from a floor of a 120-storey building is dented upon impact. A ball can be reused in fresh drops only if it has not been dented in a previous drop. Using only these two identical balls, what is the smallest number of ball drops that will determine the highest floor from which the ball can be dropped without being damaged?
The key to these type of questions is always to get the two slowest people over together. John and Kerry going over separately will take 15 mins, but getting them over together will only take 9. Once you've realised you've got to get them over together to make the shortest time, you can work the rest of the puzzle around that.
You need to get the 2 quickies over, then send one back with the canoe, then send the 2 slowies over, then the quicky left on the far bank comes back to collect the other quicky now on the near bank, and both quickies return to join the 2 slowies and complete the task.
You need to get the 2 quickies over, then send one back with the canoe, then send the 2 slowies over, then the quicky left on the far bank comes back to collect the other quicky now on the near bank, and both quickies return to join the 2 slowies and complete the task.
ILikeCake said:
Oh, maybe I should put the career change on hold
Okay if that was too easy how about this:
You are given two identical balls made of a tough alloy. The hardness test fails if a ball dropped from a floor of a 120-storey building is dented upon impact. A ball can be reused in fresh drops only if it has not been dented in a previous drop. Using only these two identical balls, what is the smallest number of ball drops that will determine the highest floor from which the ball can be dropped without being damaged?
Ooo, I've heard this one years ago, with 2 eggs and 100 floors. I can't remember the algebra, but to get the best outcome was starting at floor 15, then increasing in stages of 1 less floor each time, so floor 15, then +14 to floor 29, plus 13 to floor 42, plus 12 to floor 54, floor 65, 75, 84 and so on. The once the first egg breaks, go up in stages of 1 from the last successful drop. Okay if that was too easy how about this:
You are given two identical balls made of a tough alloy. The hardness test fails if a ball dropped from a floor of a 120-storey building is dented upon impact. A ball can be reused in fresh drops only if it has not been dented in a previous drop. Using only these two identical balls, what is the smallest number of ball drops that will determine the highest floor from which the ball can be dropped without being damaged?
Or something like that. I'm too old for all this stuff now. .
TwigtheWonderkid said:
Amy and Jim go over, that takes 3 mins.
Amy rows back alone, 1 min
John and Kerry go over, 9 mins
Jim rows back alone to get Amy, 3 mins
Jim & Amy cross back, 3 mins
Job done in 19 mins.
Am I being thick here, but when Jim & Amy cross back then that would be 1 minute and therefore a total of 17 mins?Amy rows back alone, 1 min
John and Kerry go over, 9 mins
Jim rows back alone to get Amy, 3 mins
Jim & Amy cross back, 3 mins
Job done in 19 mins.
ILikeCake said:
Okay if that was too easy how about this:
You are given two identical balls made of a tough alloy. The hardness test fails if a ball dropped from a floor of a 120-storey building is dented upon impact. A ball can be reused in fresh drops only if it has not been dented in a previous drop. Using only these two identical balls, what is the smallest number of ball drops that will determine the highest floor from which the ball can be dropped without being damaged?
Probably highlighting myself as thick, but is it "one"?You are given two identical balls made of a tough alloy. The hardness test fails if a ball dropped from a floor of a 120-storey building is dented upon impact. A ball can be reused in fresh drops only if it has not been dented in a previous drop. Using only these two identical balls, what is the smallest number of ball drops that will determine the highest floor from which the ball can be dropped without being damaged?
ie, if you drop one ball from the 1st floor, and it dents, then you wouldn't use the 2nd and you wouldn't go any higher than the 1st floor?
Wacky Racer said:
How about this one, it's surprising how many intelligent people get it wrong.
In a bedroom drawer there are 20 loose red socks and 20 blue socks.
If you went into the room in total darkness, what's the minimum number of socks you could bring out to ensure you have a matching pair?
3?In a bedroom drawer there are 20 loose red socks and 20 blue socks.
If you went into the room in total darkness, what's the minimum number of socks you could bring out to ensure you have a matching pair?
Wacky Racer said:
How about this one, it's surprising how many intelligent people get it wrong.
In a bedroom drawer there are 20 loose red socks and 20 blue socks.
If you went into the room in total darkness, what's the minimum number of socks you could bring out to ensure you have a matching pair?
Three?In a bedroom drawer there are 20 loose red socks and 20 blue socks.
If you went into the room in total darkness, what's the minimum number of socks you could bring out to ensure you have a matching pair?
Wacky Racer said:
How about this one, it's surprising how many intelligent people get it wrong.
In a bedroom drawer there are 20 loose red socks and 20 blue socks.
If you went into the room in total darkness, what's the minimum number of socks you could bring out to ensure you have a matching pair?
21In a bedroom drawer there are 20 loose red socks and 20 blue socks.
If you went into the room in total darkness, what's the minimum number of socks you could bring out to ensure you have a matching pair?
MYOB said:
Wacky Racer said:
Yes, the amount of people that say 21 is amazing...….try it on your friends.
I would have said 2. I could pick up a matching pair in the first two picks. But I'm not a maths genius! Pick a sock - its (say) Red.
Pick a 2nd sock - if its red, great, you win, game over. If its blue, you have an unmatched pair - move to round 3.
Pick a 3rd sock - whether its red or blue you now have 1 matching pair when combined with the Red from round 1, and the Bue from round 2.
MYOB said:
Wacky Racer said:
Yes, the amount of people that say 21 is amazing...….try it on your friends.
I would have said 2. I could pick up a matching pair in the first two picks. But I'm not a maths genius! ILikeCake said:
You are given two identical balls made of a tough alloy. The hardness test fails if a ball dropped from a floor of a 120-storey building is dented upon impact. A ball can be reused in fresh drops only if it has not been dented in a previous drop. Using only these two identical balls, what is the smallest number of ball drops that will determine the highest floor from which the ball can be dropped without being damaged?
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