Enigma 228: Quality control
9 October 2014
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From New Scientist #1374, 8th September 1983 [link]
At the car factory where I work the latest model is pouring off the assembly line. Their chassis numbers started at 1 and they have been numbered consecutively since.
In the quality control department we have to check some of the cars. The first one we checked was one of the early ones off the line. Then we checked all cars whose chassis numbers were multiples of the first number which we had checked.
Unfortunately this system let too many mistakes go undetected and so the manager asked us to check an extra car last week. He also introduced new rules by which we would subsequently have to check all cars whose chassis numbers were the sum of two numbers (possibly the same) which we had already checked.
Car number 77777 has just gone through unchecked and we are now checking number 77778. Our union is demanding extra staff in this department because we now realise that under the new rules we are going to have to check every car from now on.
How many of the first 77777 cars were checked?
Note: I am still waiting for a phone line to be connected at my new house, so I only have sporadic access to the internet at the moment. The latest estimate is that I’ll have a connection by the end of October 2014.