## Tuesday, April 27, 2010

### The Party is Starting Soon

You have an old-fashioned refrigerator with a small freezer compartment capable of holding seven ice cube trays stacked vertically. But there are no shelves to separate the trays, and if you stack one tray on top of another before the ice cubes in the bottom tray are fully frozen, the top tray will nestle into it, and you won't get full cubes in the bottom tray. You have an unlimited supply of trays, each of which can make a dozen cubes. What's the fastest way to make full-sized ice cubes?

1. All I can come up with for the most you can make in the shortest time is 4 trays. You fill the first tray then place a second empty tray, place a full third tray right side up on top of that, followed by empty tray upside down and so on until you have 7 trays stacked, 4 of which are full and stacked right side up, sandwiched between them are 3 empty trays facing down.

2. You're not clear on how many ice cubes you want? You could just put one tray in, and when it freezes, put the next on top, and so on until you have seven full frozen trays. Alternatively, you could place a layer of thin cardboard between each of the seven trays to stop them sinking into each other, and so get seven full trays at one go.

3. My suggestion would be to place the first tray, then wait for the surface to freeze until the ice can support the next tray and so on. But to make sure what the fastest solution is we would have to know the rate at which the freezer is able to remove heat from the water, as well as the size of the cubes.

4. i think i've got it!... I'm assuming that each of the trays nestles into the other (stacking without water in them they fit into each other (which BTW are just bad ice trays))... So you cannot stack even one on top of the other until the lower is frozen...... so here's what you do.. freeze one tray fully... then pop them out (12 cubes) place 2 frozen cubes in the opposite corners of each of the remaining six trays. this will allow you to stack them without them nestling together. use the tray you first froze on the very top to make a full stack of seven trays positioned nicely on top of each other

5. zoe and reallyfatbloke, good answers but I think you can get more at a time using Garret's approach.

Anonymous is right about needing more information to really get into the problem, since the more water you're trying to freeze probably means the longer it will take to do the freezing.

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