Puzzler of the week

[Scott MacLean]

This week's puzzler:

A farmer had a 40-pound stone, which he could use to weigh 40 pounds of feed; he would sell feed in 40 pounds, or bales of hay, or whatever. He had a balance scale; he put the stone on one side and pile the other side with feed or hay, and when it balanced, that's it.

A neighbor borrows the stone, but he had to apologize when he returned it, broken into four pieces. The farmer who owned the stone later told the neighbor that he actually had done him a favor. The pieces of the broken stone could now be used to weigh any item, assuming those items were in one-pound increments, from one pound to 40.

What were the weights of the four individual stones?

Last week's puzzler:

The other day in the shop I had two Toyota Camrys each side by side. One of them didn't run. It cranked and you turn the key and wa, wa, wa, but it wouldn't fire up. And the other one was in for an emissions test. So I tell Ralph to do these two cars. So he takes the emissions tester probe. He sticks it in the tail pipe of the car, which he is supposed to do the emissions test on. He opens the hood. The next thing I know he is cranking this car, wa, wa, wa. It won't start.

He then takes the probe out of the tailpipe, sticks it in the other car. He gets into the car that wouldn't start. And he turns the key and of course, it doesn't start. It does the same thing that the first car did. Wa, wa, wa. I say to him, "What the hell are you doing?"

I assumed at first that he went to the wrong car. He then explains to me what he is doing. I say ah ha! What's he doing?

Last week's puzzler answer:

Well, he knew that the first Camry, the one that came in for the emission's test, ran. He sticks the probe in the tailpipe, and opens the hood, and disables the ignition system so that the car will not start. So, now he basically has this car, number one, like car number two. He turns the key, and he reads the emissions on the machine. He reads it's got like 3,000 parts per million of unburned hydrocarbons. Obviously, because it won't start.

The injectors are squirting fuel and it's not getting combusted. When he puts the probe in the other car's tailpipe, he's looking to see if it has the same kind of emissions. If it does, then he knows that the fuel system's working. The pump's working, the injectors are firing off. And if he sees that there are no emissions with the same cranking time, then he knows that it's a fuel system problem, and not an electrical system problem. Pretty cute, huh?