The Valley Crossing Problem 

Problem: There are some people who have to cross a valley. They are having a long pole with them. Suggest the ways by which they can cross the valley.

Solutions:

1.       The obvious one J Put the pole on the valley and let all men cross. This solution involves equal risk for each members (assuming none is an acrobat expertJ) so looks fair and most obvious.

2.       The Leap of Faith: As the name says this solution requires each member to have trust in the solution or have full understanding of the solution so that none have any doubt.

Basic pre-requisites

a)      Minimum no of people : 3

b)      Width of the valley shall be at max 2 complete steps.

c)       Length of pole is sufficiently greater.

d)      Gap between the people is greater than or equal to the valley width.

Solution goes as:

Let L (n) and R (n) denotes the left and right leg of the peoples, let orange represent one leg of person hanging and red represent person hanging fully.

Step 1:

L(3)L(2)L(1)  

R(3)R(2)R(1)

Step 2:

L(3)L(2)                 L(1)

R(3)R(2)R(1)

Step 3:

L(3)L(2)                 L(1)

R(3)R(2)                R(1)

Step 4:

L(3)                        L(2)                        L(1)

R(3)R(2)                 R(1)

Step5:

L(3)                        L(2)                        L(1)

R(3)                        R(2)                        R(1)

Step 6:

       L(3)                        L(2)L(1)

R(3)                        R(2)                        R(1)

Step 7:

       L(3)                        L(2)L(1)

       R(3)                        R(2)R(1)

Step 8:

                                                                L(3)L(2)L(1)

                               R(3)                        R(2)R(1)

Step 9:

                                                                L(3)L(2)L(1)

                                                                R(3)R(2)R(1)

Interpretations:

1.       The “No boss model” : Assuming that the people have one common goal to cross the valley and there is no boss or authority involved then the solution has following features:

a)      Interdependent role: Each individual relies upon others for achieving the common goal for the group. The goal in this case being crossing the valley. Success of each individual depends not only upon his/her efforts but also on the efforts put in by the other members of the group. So each individual of the group being equally responsible for success/failure of the group.

b)       Cohesiveness: Each member has to work as a team with all other members to attain the common objective. In this case it is the team work which is need and not the individual excellence i.e. having a long/high jumper in the group might help but will not improve his/her chance either as jumping the valley with a steel pole might not be a wise idea JBest result will come only when each one of the group sticks to the plan

c)       Matrix structure: The present task model requires team work and interdependence so all are equals and hence anyone can command anyone, no hierarchy exists no single bell rings each one listens to each other. So if the group has got a Judge, a thief and a manager then the thief can command the Judge and manager will have to adhere to the group objectives.

  Such systems result into systems of excellence as each member strives for one common goal which is the group goal. Even though the group goals may me risker but the understanding being risk being risk and opportunity being same for all.

Had there being a central command which would have drawn such a plan priory and explained it to the set of people and asked the group to perform the task; there would have being a fair amount of suspicion amongst the group members. And the group might be just a mediocre collection of highly talented individuals.

Ankur Shree
Nitie IM-19
Roll: 220