Find the bogus coffee bean! (riddle)

[Spencer]

The mail arrives and you get a package from your expert roaster. In it you find sixteen coffee beans. There is also a note from the roaster. The beans are a rare single origin that you ordered, but the roaster states that one stray bean fell into the mix. All the beans are identical in appearance, but because the rare beans are especially light, he knows that the stray bean is heavier.

Your joy at the arrival of the rare beans gives way to concern. You are pulling a ristretto shot for malachi and know that he will immediately discern the impurity of the sixteenth bean. There is a coin operated balance and you have enough coins to weigh the beans three times. Can you separate out the stray bean and make the pure shot, and if so, how?

[lino]

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Take two beans out. Weigh the remaining 14, 7 per side.
If the 7 and 7 balance, weight the two that were set aside against each other. Discard the heaviest. Make coffee for malachi.
If the 7 and 7 don't balance, set aside the light 7 with the original two.
Set aside one of the heavy 7 (by itself)
Balance 3 and 3.
If they balance, the one you set aside is bad. Use others to make coffee for malachi.
If they do not balance,
Set aside light 3 into good pile.
Pick one of heavy three and put it aside by itself.
Weigh remaining two.
If they balance, one aside is bad.
If they don't throw away heavy one.
Make coffee for malachi.

ciao

lino

[HB]

Lino's right! Some may recognize Spenser's puzzle as a variant of The Counterfeit Coin.

[MarkJ]

OK, first make two piles of 8 and find the heavy pile (1 coin used).

Then remove 2 beans and compare the remaining 6 beans as two piles of 3 (second coin).

If they weigh the same, then one of the removed 2 is the heavy bean so compare those to find the heavy bean (third coin).

If they do not weigh the same, you now have 3 beans, one of which is the heavy one. Remove one and compare the others--if one is heavier, that's the suspect bean. If not, the removed single bean is it.

Nice little problem!

Mark

[shadowfax]

My only problem is, if the beans are especially light, and you only have 15, how are you going to get enough to make a shot for Chris?

[Psyd]

You're the super. You're the extremely lazy super. The stairwell light switches for the three storie tenement that you are the super for, are located in your basement 'office'. 'Coz you're lazy. They're smoked. Completely useless. When you removed the switchpanels, you discovered a blackened, melted mass.
Well, you've finally gone out and bought new switches (you were outta smokes, so you were going out anyway) and you've procrastinated as long as you can. Problem is, it's been so long since you took out the old ones to see where the smoke was coming from, that you've forgotten which wire goes to what floor.
Now, you only want to wire them once, but you're pretty sure that you're not going to get that lucky, 'coz that's how your life has been going so far. How are you going to make sure that you only have to climb the stairs one time to see if you got it right, and if you didn't, that you don't have to climb the stairs again once you re-wire?

[Psyd]

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Wire 'em up any old way, and turn one and two on. Sit down and have a smoke. Once you're done with the smoke, turn one off and climb the stairs. Two is the one that's lit, One is the one that's dark and warm, three is the one that's dark and warm. If you're smart and lazy, you only have to climb two flights.