Question 1132375: 2017 soldiers were lined up in a file. The commander ordered them to number off 1,2,3,4,5,1,2,3,4,5,1... starting from the first soldier. He then ordered them to number off 1,2,3,4,1,2,3,4,1... starting from the last soldier. How many soldiers had the same number both times?
Found 2 solutions by ikleyn, Alan3354:
Answer by ikleyn(52754)   (Show Source):
You can put this solution on YOUR website! .
2017 soldiers were lined up in a  line.
The commander ordered them to number off 1,2,3,4,5,1,2,3,4,5,1... starting from the first soldier.
He then ordered them to number off 1,2,3,4,1,2,3,4,1... starting from the last soldier. How many soldiers had the same number both times?
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Pay attention on how I edited your post . . .
Separate 2017 soldiers lined up in a LINE, in segments of 20 soldiers each.
In each such segment you have these sequential numbers
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 (1)
1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 (2) counted by 5
1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 (3) counted by 4
As you can see, in each segment of 20 soldiers, only 4 first soldiers have equal numbers.
 = 100.85.
It means that there are 100 such segments of 20 soldiers, in all, PLUS part of the 101-th segment,
consisting of 17 soldiers.
It implies that the ANSWER to the problem's question is THIS NUMBER
4*100 + 4 = 404 soldiers.
ANSWER. 404 soldiers.
Solved.
Answer by Alan3354(69443)  (Show Source):
You can put this solution on YOUR website! Soldiers always line up "alphabetically by height."
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- Yogi Berra's statement about lining up.
Don't want to plagiarize.
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