Making Ice

[BMAD]

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?

[vigmeister]

should be in a tray to prevent the tray above it from ruining the cubes below?

Assuming 4, then I would make 1 tray of cubes and then use it to make 3 trays with 4 cubes each and fill those with water with another tray with only water on top.

This will then give us 36 cubes. Again I put in 24 cubes in 6 trays to prop them all up and one tray of water on top.

This gives me 60 cubes in this cycle. Rinse and repeat for 60 cubes in each cycle...

[bgm1961]

vigmeister's solutions is probably the one you're looking for. But alternatively you could get right down to business by:

Put six trays at a time in the freezer, each seperated by a thin piece of cardboard or bamboo skewers. Then you can fill each tray to full and freeze 72 cubes at a whack! Again, don't think it's the answer you were looking for, but it would work.

[BMAD]

vigmeister's solutions is probably the one you're looking for. But alternatively you could get right down to business by:

Put six trays at a time in the freezer, each seperated by a thin piece of cardboard or bamboo skewers. Then you can fill each tray to full and freeze 72 cubes at a whack! Again, don't think it's the answer you were looking for, but it would work.

you are on the right track but i am looking for a bigger answer (and assume you have nothing more than trays (no bamboo )

[maheshrvyas]

I can think of a way of making full sized cubes but this may not be the fastest one.

Put 1 in freezer, once it freezes, take out that one, put another one, invert the 1 which is already freezed and put 1 more over it, .... and so on.

[BMAD]

I can think of a way of making full sized cubes but this may not be the fastest one.

Put 1 in freezer, once it freezes, take out that one, put another one, invert the 1 which is already freezed and put 1 more over it, .... and so on.

We are looking for the most ice cubes frozen on a single freezing try

[kingofpain]

That the number of minimum cubes to prop up a tray is irrelevant in this case then

Another approach is to put one tray in and wait until the surface freezes and add another tray and so on...

Combine this with the concept of three inverted trays sandwiched in between trays of water and you can get a lot of ice cubes in a slightly longer time that a cycle

[bgm1961]

Hmmm... you made it clear that we're working with a small freezer capable of holding only seven trays, but...

You said that the freezer holds seven ice cube trays stacked vertically. But you never mentioned its horizontal dimension. Without using Bamboo

, the best way is to stack the trays is in a criss-cross fashion, or perpendicular to each other, given that the freezer is wide enough to fit the full length of a tray.

[BobbyGo]

Since you have an unlimited supply of trays...

Could you use the extra trays as separators? They could be broken apart and wedged in along the edges just enough so that the trays on top do not dip into the ones underneath. Or possibly even used to prop up the trays "card-house style".

[Morningstar]

Freeze one tray fully, then take all the ice cubes out except two, one in one corner and one in the opposite corner. Put two cubes in each tray in the same pattern, fill them all with water, and balance them on top of each other using the already-frozen cubes as supports.

[BMAD]

I think one of the problems with this problem is that we are missing the assumption that standard ice trays hold 12 ice cubes

[ShadowAngel7]

I think one of the problems with this problem is that we are missing the assumption that standard ice trays hold 12 ice cubes

That's not what's missing--you said in the OP that each tray holds a dozen.

[BMAD]

You can make 120 cubes (10 full trays) in the time it takes to freeze two trays. First, fill four of the trays with water and turn the other three upside down and use them to space the four apart. That gives you 48 cubes. Next, empty the four trays and put two ice cubes in diagonally opposed corners of each of six of the trays. Fill the remaining holes -- and the entire seventh tray -- with water. Using the ice cubes to hold the trays apart, stack all seven (the seventh tray should go on top), and freeze them. You'll get an additional 72 cubes. You can get 72 cubes for every batch except the first, for which spacer ice cubes are not yet available.

[kingofpain]

Vigmeister and I collectively had the same solution then in separate posts. I would combine it with the 'surface freezing concept' to go even faster! Vigmeister assumed you need 4 cubes to hold up a tray though and someone else came up with the 2 cube idea...

However vigmeister and I are the same person, so I claim the solution