Brainteasers – Issue 21, 2011
1. Queue See
The non-automated assembly line at Widgets”R”Us is notorious for its uneven quality – and its eccentric QC inspectors. After a full day’s production the three person Quality Control team evaluated the finished parts. Lisa initially flagged half of all the parts as defective, but on further inspection she cleared 10 of the suspect parts. Tim reviewed all the parts passed by Lisa and flagged one third of them as defective, but then he was able to fix two of them. The last inspector – Sally – flagged one fifth of the remaining parts, but then changed her mind about one of them and cleared it. After these inspections the factory was only able to ship 17 parts for the day. What was the total number of parts (good and bad) for the day’s production run?
A rotary indexing table has nine workstations positioned around its perimeter. The workstations are located at 15°, 40°, 60°, 110°, 135°, 200°, 275°, 325°, & 350° respectively. The motion control system driving the table can be programmed for only two move distances (in degrees), but those moves can each be made in either direction. For accuracy all the moves must originate at the home position (0°). What are the two move distances that will allow the table to reach all the workstation positions with the shortest number of total moves? (The moves required to return to the home sensor don’t count.) For example: moves of 125° and 75° would work and could reach all the workstations with a total of 28 moves – but there is a better solution.
This motion control system could certainly benefit from the flexibility of a SureServo™ system from AutomationDirect!
3. One-Lane Highway
You have N cars that are all traveling the same direction on an infinitely long one-lane highway. Unfortunately – but typically – the drivers would all prefer to go different speeds, but they cannot pass each other. So eventually the cars will group up in one or more clumps.
In terms of N, what is the expected number of clumps of cars?