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# Pull & Push

## Question

Rearrange some or all of the lockers on the middle of the locker room (as shown)
in order : left to right-top to bottom. How should it be done in energy saving way?

## Recommended Posts

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Do they need to end in the same 6 spaces, or can they end in a new position (as a group)?

These are the fewest that I've found so far:

Label maker - 0 moves

End up elsewhere - 10 moves

End in same as began - 12 moves

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Can we assume gravity as a free move? If i move locker number 1 out will locker number four safely move with gravity on top of number five?

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How about 10 moves to get them in the required order in the center of the room.

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Can we assume gravity as a free move? If i move locker number 1 out will locker number four safely move with gravity on top of number five?

I believe that it is an overhead view so all of the lockers are sitting on the ground in the center of the room.

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Do they need to end in the same 6 spaces, or can they end in a new position (as a group)?

These are the fewest that I've found so far:

Label maker - 0 moves

End up elsewhere - 10 moves

End in same as began - 12 moves

I got 10 moves for both ending up elsewhere and ending up in the same place.

If you push the 2 up and the 4 right, and the 5 down and the 3 left, you get this:

2

4

1 6

3

5

So at this point you can sort of choose whether you want it to be elsewhere or in the same place in six more moves.

Question: Are we allowed to arrange them in 3 by 2 or 1 by 6 or 6 by 1 rather than 2 by 3? Also, do they have to be packed in a grid, or can they be staggered such as in the spoiler above?

Edited by gavinksong
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The expected middle position is same as shown in the OP. Only the numbers should be rearrange with [ 1 ][ 2 ] on top , [ 5] [ 6 ] on bottom (left to right-top to bottom)
We know that pull=push and up/down is less work than left/right..thus some 10 moves can be less effort than other 10 moves.. yet not good enough

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Do they need to end in the same 6 spaces, or can they end in a new position (as a group)?Yes,No

These are the fewest that I've found so far:

Label maker - 0 moves Labels are painted on the "doors"

End up elsewhere - 10 moves It can end elsewhere in less moves.

End in same as began - 12 moves You mean began as the left to right-top bottom arrangement? That is right!

for 5 moves it looks like..

then 4, 1 , 3 , 6, 5, 4, 2

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