Gathering Potatoes
At the annual Puzzlarria picnic, there is lots of fun and games.
Scenario:
A basket, large enough to hold 100 potatoes is placed on the ground. Beginning 10 feet from the basket, and in a straight line, a potato is placed every 10 feet ... a total of 100 potatoes. A prize, of a night of free beverages at the Puzzlaria Tavern, is offered to the FIRST person who correctly answers the question:
If a person gathers all the potatoes, one at a time, and places them in the basket, how far would he or she travel? (for clarity, each potato gathered must be placed in the basket before gathering another)
Game:
Ross and Curtis were selected in a random drawing to participate in the POTATO GATHERING CONTEST. Because Ross is 2.04% faster than Curtis, he offers to allow Curtis to gather one potato and drop it in the basket before he begins to gather. For clarity, Ross will have to gather 50 potatoes before Curtis can gather his remaining 49. The results of the race will vary depending on which first potato Curtis gathers and places in the basket.
Which potato should Curtis gather first to increase his chance of winning, and if he chooses correctly, by how much would he win? (for clarity, each potato gathered must be placed in the basket before gathering another ... and there is only one line of 100 potatoes, 10 feet apart ... so each participant is gathering from the same line of potatoes)
Scenario:
A basket, large enough to hold 100 potatoes is placed on the ground. Beginning 10 feet from the basket, and in a straight line, a potato is placed every 10 feet ... a total of 100 potatoes. A prize, of a night of free beverages at the Puzzlaria Tavern, is offered to the FIRST person who correctly answers the question:
If a person gathers all the potatoes, one at a time, and places them in the basket, how far would he or she travel? (for clarity, each potato gathered must be placed in the basket before gathering another)
Game:
Ross and Curtis were selected in a random drawing to participate in the POTATO GATHERING CONTEST. Because Ross is 2.04% faster than Curtis, he offers to allow Curtis to gather one potato and drop it in the basket before he begins to gather. For clarity, Ross will have to gather 50 potatoes before Curtis can gather his remaining 49. The results of the race will vary depending on which first potato Curtis gathers and places in the basket.
Which potato should Curtis gather first to increase his chance of winning, and if he chooses correctly, by how much would he win? (for clarity, each potato gathered must be placed in the basket before gathering another ... and there is only one line of 100 potatoes, 10 feet apart ... so each participant is gathering from the same line of potatoes)





11 Comments:
(1+100)/2*100*10*2=101,000'
Biggest lead is last potato. 100*10*2'=2000' lead
d=v/t
d1=101000-2000=99000
t=v/d=v1/99000
d2=v2/t=1.0204*v1/t
d2=1.0204*v1/(v1/99000)=99000*1.0204
d2=101019.6'
OR
d2=101000
d2=1.0204*v1/t
t=101000/(1.0204*v1)
d1=v1/t=101000/1.0204=98980.79'
99000-98980.79'=19.21' shy of finishing when Ross does.
Must be some error in my interpretation. But I can't spot it.
Cam
Meh. Please disregard last post.
d != v/t d=v*t
Cam
Total distance to gather 100 potatoes:
(1+100)/2*100*10*2=101,000'
Biggest lead is last potato. 100*10*2'=2000' lead
d1=v1*t
d1=101000-2000=99000
t=d1/v1=99000/v1
d2=v2*t=1.0204*v1*t
d2=1.0204*v1*(99000/v1)=99000*1.0204
d2=101019.6'
OR
d2=101000
d2=1.0204*v1*t
t=101000/(1.0204*v1)
d1=v1*t=v1*101000/(1.0204*v1)=98980.79'
99000-98980.79'=19.21' shy of finishing when Ross does.
Right calculation this time, but same result. Likely some error in my interpretation. But I can't spot it. Almost embarassed to post this.
Cam
I think I properly read the question this time.
Curtis gather potato 100
When they start the race Ross being faster gets to potato 1 leaving Curtis potato 2...
Curtis must gather evens, Ross gets odds.
Curtis must cover
d1=(2+98)/2*49*10*2=50*50*10*2=49000'
Ross must cover
d2=(1+99)/2*50*10*2=50*50*10*2=50000'
d1=v1*t
49000=v1*t
t=49000/v1
d2=v2*t=1.0204*v1*t
d2=1.0204*v1*(49000)/v1=49999.6'
50000-49999.6'=0.4'
Answer:
Curtis wins by 0.4'
Cam
Sorry about the sloppy answers guys. Going for coffee now.
Cam
good work Cam ... problem source says he will win by less than half a foot .... you certainly agree.
Cam ... did you answer the question about how far a person would travel in gathering and basketing (<- new word :)) all the potatoes, one at a time?
Glad I was successful in the game as I had no idea on the solution!!
However
for 1 person collecting potatoes
(n+1)/2 * d * 2 * n = total distance travelled, assuming a start at the basket
n=number potatoes
d=distance between potatoes
(100+1)/2 * 10 * 2 * 100 = 101,000
regards, Curtis
you're right Curtis
Thanks for the "Meh" and the "coffee", I've been missing them lateley. LOL.
Hi Zaux
Just had another look at the "game"
It appears to me that if the 1st potato is selected, curtis still wins by 0.408ft
curtis would need to travel 49980ft
ross would need to travel 51000ft
but 49980 x 1.0204 = only 50999.592ft .......so ross loses
perhaps the result is the same for any potato selected.
regards, Curtis
Now that my head is on straight
Look at the best potato to take.....
Curtis takes potato 1
Curtis must cover
d1=(3+99)/2*49*10*2=51*49*10*2=49980'
Ross must cover
d2=(2+100)/2*50*10*2=51*50*10*2=51000'
d1=v1*t
49980=v1*t
t=49980/v1
d2=v2*t=1.0204*v1*t
d2=1.0204*v1*(49980)/v1=50999.6'
51000-50999.6'=0.4'
Answer:
Curtis wins by 0.4'
Curtis takes potato #2
Ross gets potato 1 first , Curtis gets 3 and the other odds, Ross has to switch to evens
1=R
2=XgoneX
3=C
4=R ....
Curtis must cover
d1=(3+99)/2*49*10*2=51*49*10*2=49980'
Ross must cover
d2=1*20+(4+100)/2*49*10*2=20+52*49*10*2=50980'
d1=v1*t
49980=v1*t
t=49980/v1
d2=v2*t=1.0204*v1*t
d2=1.0204*v1*(49980)/v1=50999.6'
50980-50999.6'=-19.6''
Answer:
Curtis loses by 19.6'
Curtis takes potato #3
Ross gets potato 1 first , Curtis gets 2 and the other evens, Ross gets potato 4 and switches to evens, Curtis is forced to switch to odds
1=R
2=C
3=XgoneX
4=R
5=C .....
Curtis must cover
d1=2*20+(5+99)/2*48*10*2=40+52*48*10*2=49960'
Ross must cover
d2=2*10+(4+100)/2*49*10*2=20+52*49*10*2=50980'
d1=v1*t
49960=v1*t
t=49960/v1
d2=v2*t=1.0204*v1*t
d2=1.0204*v1*(49960)/v1=50979.2'
50980-50979.2'=0.8'
Answer:
Curtis wins by 0.8'
The above are examples. Crunching the numbers for all the possible potatoes that Curtis could take.....
All even numbered potatos are losers for Curtis except 100, where he wins by 0.4'
-the amount he loses by reduces as the # of potato increases,until he edges out a slight win at 100
All odd potatos are winners,the smallest he wins by is 0.4' with potato 1. The largest he can win by is 20.4' by taking potato 99. d1=49000, d2=50020, 1.0204*49000=49999.6,50020-49999.6=20.4'
Cam
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