## Tuesday, March 30, 2010

### Kiss the Cook

You awake one morning to find the power out. Again. Of course, this isn't a problem since you have devised numerous methods of timing all your dishes to cesium precision using only two hour glasses. Unfortunately, two shipments of ingredients have just come in. One shipment is twelve boxes containing eggs, the other is twelve boxes containing flour. You need the flour right away, but without proper refrigeration the eggs will go bad. The eggs will be fine in their boxes, but if you open a box of eggs looking for the flour, those eggs will be wasted.

The boxes are indistinguishable by appearance- your supplier uses the same boxes for both. Also, the supplier's packing standards are not particularly high. Not only may the eggs break if your examination of the boxes involves high-speed collisions, but each box of the shipments do not have a constant quantity inside.

This is what you know:

The flour is all-purpose bleached flour
The eggs are Grade A Extra Large brown
The lightest box weighs 47.85 ounces
The heaviest box weighs 65.63 ounces
An empty box weighs 5.02 ounces
The kitchen scale is accurate to 1/100th of an ounce.

How can you safely choose a box containing flour without the risk of accidentally opening a box of eggs?

#### 2 comments:

1. You might want to kiss the box - and see if some are colder than others. They would be the eggs which were refrigerated. So the warmer ones would be the flour.

2. I guess that would depend on the room temperature, how long the boxes have been sitting there, what there original temperature was, and a whole host of other factors...(did they spend any time outside between being dropped off?)

I'm not saying it wouldn't work, but it might not.

The answer as given here http://www.greylabyrinth.com/solution/puzzle016:

Weigh the each individual case in the two shipments, and note the individual weights. The boxes all weighed between 40 and 60 ounces. This means that we can expect the egg boxes to contain around two dozen eggs (more or less), since an extra large egg weighs a little over 2 ounces.
The useful data we're looking for in weighing the packages is the weight breakdown. Whichever boxes contain flour will weigh random amounts between 40 and 60 ounces. The eggs, however, must weigh in at discrete intervals. The smallest difference for boxes in the egg shipment will be equal to the weight of a single egg (plus or minus a small amount depending on the eggs). The flour's smallest interval is the weight of one grain of flour.

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