james@ur-laser.uucp (James Chavin) (08/23/84)
---ritual sacrifice to the phantom line eater---
The team which brought you witches and eggs presents:
LIFE-OR-DEATH-LOGIC
Mr. Explorer is off to an outpost at the north pole that is a six-day
hike from Alaska across a desolate expanse of snow and ice. One man can carry
only enough food and supplies for four days. Obviously, one man can't go alone
because his supplies would not last for the complete journey. What is the
minimum amount of people that it would take to assure that Mr. Explorer reaches
the out post and all his assistants make it back to Alaska?
The solution will be given by Monday or it can be found in a book called Diabolical Diversions by Bragdon Fellows.
James Chavin and Gary Krakower
Laboratory for Laser Energetics
University of Rochester
250 East River Road
Rochester, N.Y. 14623
{allegra,seismo} !rochester!ur-laser!james
~gupta@asgb.UUCP (08/25/84)
Here is the solution:
Let the amount of food that is needed by a person for one day be 1
unit. Each person can carry 4 units.
Also let,
+-------+-------+-------+-------+-------+-------+
0 1 2 3 4 5 6
HOME FINAL DESTINATION
represent the journey. Each number represents the number of days it
takes to reach it from home.
16 people start (including the explorer) with 64 units of food and
travel for one day. At the end of the day, they have 48 units of food
left.
On day two, 8 people (party 1) take 8 units of food and return home.
The other 8 take 32 units with them and leave 8 units for consumption
on the way back. At the end of the day, they have with them 24 units
of food left. Also, "party 1" reaches home.
On day three, 4 people (party 2) turn back with 4 units of food, and
the other 4 take 16 units with them and leave 4 units behind. At the
end of the day, they have 12 units of food left. Also, "party 2" is
only 1 day away from home and finds the 8 units food left by them on
day two. Their food is gone.
On day four, 2 people (party 3) separate from the main party and turn
back with 2 units of food. The other 2 take 8 units of food and leave
2 units behind. "Party 2" takes 4 units of food from the hoard it finds
and leaves the 4 units behind. At the end of the day, the main party
has 6 units of food left with them, "party 2" has reached home.
At this point the food and people situation is as follows:
"Party-3"
|
People 2 - 2
Food 4 4 2 6
+-------+-------+-------+-------+-------+-------+
0 1 2 3 4 5 6
HOME FINAL DESTINATION
On day five, "party 3" takes 2 units of food for their consumption
and continues its journey homeward. The explorer takes 4 units of food
and continues towards the destination. The explorer's partner takes 1
unit of food and turns back. They leave 1 unit of food at point "4".
At the end of the day the situation is as follows:
"Party-3" "Partner" "Explorer"
| | |
People 2 - 1 - 1
Food 4 2 2 1 3
+-------+-------+-------+-------+-------+-------+
0 1 2 3 4 5 6
HOME FINAL DESTINATION
On day six, the "party 3" takes 2 units of food and heads home.
The partner takes 1 units of food and continues homeward and
the explorer continues towards the destination. At the end of the
day, the "party 3" has reached home, partner is at point 2 and
the explorer is at the detination. The food situation is as follows:
"Party-3" "Partner" "Explorer"
| | |
People 2 - 1 - - - 1
Food 2 2 1 1 - 2
+-------+-------+-------+-------+-------+-------+
0 1 2 3 4 5 6
HOME FINAL DESTINATION
From now on, the partner just keeps going taking 1 unit of food
from each point and the explorer on his way back has 2 units of
food to last him till point 4 and from then on each location has
1 unit of food.
Answer: So, the explorer starts of with 15 extra people.
ps. Kind of a dumb explorer if he goes through all this trouble and
does not even spend a day at the destination. So, another question:
How many people will he leave with if he has to stay at the destination
for 1 day? 2 days? N days?
Yogesh Gupta {sdcrdcf, sdcsvax} !bmcg!asgb!guptamarkb@sdcrdcf.UUCP (08/27/84)
The original problem does not require that the explorer return to alaska.
Therefore, the explorer needs only two associates to make it to the north
pole. The three men start out with 12 units of food. After traveling 1 day,
one gives a unit of food to each of the others (they now have 8), takes
his one remaining unit of food and returns. After another day of travel
the explorer take 4 units of food (enough to get ot the base) and goes on
leaving 2 units for the other man to use to return.
Mark Biggar
{allegra,burdvax,cbosgd,hplabs,ihnp4,akgua,sdcsvax}!sdcrdcf!markb