Ernie and the disappointing drill bits

I was driving to Ernie's place a couple of days ago, with Ernie in the passenger seat, when we drove past an old building with a faded sign reading Lar's Tool's. Beneath it, scrawled on the front wall of the shop in white paint, a second sign read Closeing down sale - last day's - 75% of all tool's (clearly Lars' specialty was not grammar or spelling). Ernie, always keen for a bargain, asked me to stop for a quick look. Inside, the gloomy workshop was packed with scarred old tables heaped with an assortment of dusty equipment. Lars (presumably) was the elderly gentleman sitting beside a battered cash-register. Ernie asked me to check out a table labelled Loose Drill bit's while he investigated a pile of antique bench-vices.

I was pleasantly surprised to find that underneath the dust many of the drill bits appeared to be sharp and unused and I was able to sort out two identical sets of seven Acme Industry metal-working drill bits, each consisting of a 1 mm, 2 mm, 3 mm, 4 mm, 5 mm, 6 mm, and 7 mm bit. I carried them over to Lars and paid the "$1 per bit, cash only" that he requested. When I enquired if he had box to put them in Lars told me somewhat gruffly that the place wasn't a box shop so he didn't have any boxes. But he then handed me a roll of duct tape and directed me to a table down the back of the shop that was laden with various off-cuts of metal tubing of assorted materials and dimensions. "Maybe you can put the drills into a couple of those tubes".

After a bit of experimentation I chose two suitably-dimensioned metal tubes, placed a complete set of seven drill bits (sizes 1,2,3...7 mm) into each, and sealed the ends off with duct tape. I went back to Lars and paid for the tubes "10 c each" (the duct tape was free, it seemed) and then returned to the car with Ernie - he hadn't found any other bargains in the shop. Back at Ernie's place I handed him the two tubes. He shook each one, then peeled the duct tape off one end of each tube in turn and looked down at the drill bits inside. "That's interesting.", said Ernie, "One of the tubes has precisely the largest possible internal diameter to be able to hold the set of seven drills such that none of them are able to rattle from side to side. The other tube has precisely the smallest possible internal diameter to be able to hold the set of drills such that at least one drill can rattle from side to side". But when he tipped the drills out onto his work-bench for a closer look things did not appear so promising. "Hmmm," he said, "I can see why the bits were only a dollar each. I am pretty sure they are cheap Acne Imdustry knock-offs of the real thing. They are unlikely to keep a good edge. But thanks for the thought anyway." I was a bit disappointed for letting him down on what I had thought to be such a bargain, but Ernie told me not to worry and that they would be useful for something. So, we had afternoon tea, chatted a bit, and then I headed home for the evening.

I didn't think any more about the day's events until Ernie phoned me with excitement in his voice yesterday morning. "That stuff you got from the tool store - the drills were rubbish, but the thin-walled stainless-steel tubes you packed them in are perfect - exactly the right internal diameters I need for my next experiment". He went on to explain how the tubes were non-standard diameters and he hadn't been able to source similar stock from his usual laboratory suppliers but thought that perhaps there could be some more identical tubes at Lars' place. "They don't have to be exactly identical", he continued, "so long as they have the same internal diameters to the nearest micron". I promised that I would have a look and hung up the phone before realising that Ernie hadn't told me what the two required internal diameters actually were.

I have tried ringing him back but he isn't answering - probably deep in thought in his lab with the phone off the hook. I could keep trying to contact him - Ernie usually leaves his lab within a few days, but I'm concerned that that the shop might have finally closed down permanently if I delay too long. All I can think of is that Ernie's comment regarding how the drills were packed into the tubes might offer a clue regarding their dimensions. Can anybody help?

* This article was originally published here