# Enigmatic Code

Programming Enigma Puzzles

## Tantalizer 472: Regular soldiers

From New Scientist #1023, 21st October 1976 [link]

The republic of Popularia has the largest police force and the longest pedestrator in the world. The latter is a moving pavement which rolls at uniform speed in both directions between the Palace of Justice and the Ministry of Fun. Rolling along with it are armed guards, standing stiffly at attention and posted at regular intervals.

If you too stood at attention on the pedestrator and timed one minute, starting and ending half way between two guards coming the other way, you would be surprised how many guards rolled past you during the minute. Or perhaps you would not. Anyway the number would be eight times the speed of the pedestrator in miles per hour.

You probably long to know the speed of the device. But that is a state secret. So you will have to be content to discover how far apart the guards are posted.

This issue of New Scientist also contains an article of the computer assisted proof of The Four Colour Theorem.

[tantalizer472]

### One response to “Tantalizer 472: Regular soldiers”

1. Jim Randell 27 September 2017 at 9:20 am

Considering relative speeds, the situation is the same as if I am stationary and the guards are on a pedestrator going at twice the speed.

So, if I count n guards, at a distance d apart, in 1 minute, then the speed of the (original) pedestrator is nd/2 per minute.

If d is measured in miles, this speed is 30nd miles per hour.

But the number of guards counted, n, is 8× the speed in miles per hour:

n = 8×30nd
n = 240nd
d = 1/240 miles

And 1 mile is 5280 feet.

Solution: The guards are 22 feet apart.

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