Issue 45, 2021

# Brain Teasers – Issue 45, 2021

A robotic applicator needs to extrude a gasket in the above shape without stopping the flow of the gasket mate- rial – or retracing any of the lines. The robotic arm can start and end the extrusion at any position along the path. Can you find the path that will allow a continuous extrusion for the gasket?

## Circular Reasoning

An eccentric factory owner has a large circular conveyor measur- ing 27 feet in circumference in the center of his factory. She wishes to place 6 sensors in positions around the conveyor such that one sen- sor or another is at a distance of one, two, three… up to twenty six feet from some other sensor. In other words, she wishes that all the integer value distances from one to twenty-six feet will be measurable between some pair of the sensors. Where should she place the sensors?

Extra Credit: How much longer could the circular conveyor be, and still allow placement of the 6 sensors with all the integer distances represented (up to the new-circumference-distance less one foot)?

## Goofy Golf

A certain nine-hole golf course has the following yardages for each hole: 300, 250, 200, 325, 275, 350, 225, 375, & 400. If a golfer could hit one of exactly two distances on every stroke, so that the ball would go directly toward the hole, pass directly over the hole, or go in the hole – what two distances would be optimal for play- ing the course with the fewest number if strokes? For example, the two distances of 125 yards and 75 yards would get a golfer around the course with 28 strokes – but this is not the lowest score possible?

## ABCs for AGV

The puzzle factory’s four Automated Guided Vehicles (AGVs) all leave their charging stations one morning for their first pickups. A is to pick-up at location A, B at B, and so on. But the owner of the fac- tory has stipulated that none of the AGVs should cross the path of any other, on this first trip. Can you find a path for each AGV that will get it to its destination, without crossing the paths of the other AGVs (or leaving the confines of the factory: the outer border)?

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