Twenty recruits stand in a long column, one behind the other. At a signal from the sergeant, the recruits standing in places 10 and 20 step forward into places 1 and 2 respectively and the others steps back. Find the least number of these maneuvers that must occur before the recruit originally in place 1 will be in place 1 once again.
Answers
Given : Twenty recruits stand in a long column, one behind the other. At a signal from the sergeant, the recruits standing in places 10 and 20 step forward into places 1 and 2 respectively and the others steps back.
To Find : the least number of these maneuvers that must occur before the recruit originally in place 1 will be in place 1 once again.
Solution:
A is at 1
After 1st change
A will be at 3rd
After 2nd change
A will be at 5th
After 3rd change
A will be at 7th
After 4th change
A will be at 9th
After 5th change
A will be at 11th
After that on each change A' position will be changed by 1
as position 10th is already ahead of him
9 more changes makes A at 20
After 14th change A will be at 20th
in 15th change A will be back to origin position
15 is the least number of these maneuvers that must occur before the recruit originally in place 1 will be in place 1 once again.
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