# Wizard of subsets

Can you change this

into this

in three moves?

You are the wizard of subsets. With only your mind, you can grab any subset of the 16 stone blocks and move them one unit in any direction (north, east, south, west). However, you may not cause two stone blocks to occupy the same space. (That's next-level wizardry!)

Let's solve this one together to see how it's done:

Now it's your turn. Can you change this

into this

in three moves?

• @ACD — A move means you grab any subset of the stone blocks (highlighted in white) and move them one unit north, east, south, or west. In the example, move #1 is three stones slid north, move #2 is three stones slid south, and move #3 is eight stones slid west. Mar 27, 2023 at 13:47
• I like the concept, but given multiple different answers, the puzzle presented is too easy. The walk-through example seems better, though it also has more than one solution. Mar 27, 2023 at 20:57
• @DanielMathias — Thanks, Daniel. There are a lot of really difficult problems posed on this site, so sometimes it's refreshing just to have a simple, easy, slightly non-intuitive problem for everyone to enjoy. Nice alternate solution, by the way. Mar 27, 2023 at 21:18
• I wonder if it's even possible to create an example with only one solution. I'm also afraid that once you've got the hang of it solving any one of these will be trivial, although I'm curious if you can actually make more challenging ones
– Ivo
Mar 28, 2023 at 6:33
• @Ivo — You're asking the same questions I've been asking myself since I started this project! Mar 28, 2023 at 12:26

Unless I'm missing something

Label the blocks left to right; top to bottom 0-F. Select the subset A-F; move it two spaces East and one space North.

 #0 #1 #2 #3    1) # # # #      2) # # # #        3) # # # #
#4 #5 #6 #7       # # # #         # # # #           # # # # # #
#8 #9 #A #B       # #   # #       # #     # #       # # # # # #
#C #D #E #F         # # # #           # # # # 

• This is a great solution! It is the most intuitive and comprehensible to humans, because it breaks off a single chunk and keeps that chunk intact as it moves it around. Mar 29, 2023 at 0:24

 l l l l
l l r r
l u u r
u u u u

Move those marked l to the left, then the rs right and then the us up.

1) l l l l      2) l l l l        3) l l l l
l l   r r       l l     r r       l l u u r r
l   u u r       l   u u   r       l u u u u r
u u u u         u u u u

• Nice, clear solution! Unfortunately, I have three correct answers, so I have to choose the one which was posted first. Mar 29, 2023 at 0:25

Very similar to @loopy-walt solution, but still OC :)

• Outstanding! This is the only solution which achieves the goal by moving 16 stones overall, which is the minimum predicted by my computer program. Unfortunately, I have three correct answers, so I have to choose the one which was posted first. Mar 29, 2023 at 0:22
• @SlowMagic loopy's solution also moves 16 stones, and each stone only once. Mar 29, 2023 at 15:20
• @justhalf — I count 18 total stone moves: step #1 involves 9 stone moves, step #2 involves 3 stone moves, and step #3 involves 6 stone moves. (And the u's move twice.) Mar 29, 2023 at 15:38
• @SlowMagic step 1 only has 7 stones moving. And each stone only move once, including the u's. Mar 29, 2023 at 15:41
• @justhalf — Aha, the complement!! You're right. Mar 29, 2023 at 15:43