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It's that time of the year*, and Santa is delivering presents to all the good children of the world.

*Almost, since the fortnightly challenge is a tad late :)

Informed by his elves that his sacks are space inefficient, Santa has decided to trial groundbreaking orthogonal sacks that are solid and compact. Leaving the packing up to the elves, as always, Santa set off on Christmas Eve carrying these solid sacks, which admittedly helped reduce the space required in his sleigh from an extremely absurd and impossible amount of space down to a somewhat absurd and impossible amount of space.

However, upon arriving at his first house, Santa realized that it was actually quite difficult to remove the presents from these sacks. The elves had packed the presents in strange, strange ways, and now it was up to him to get them back out of the sacks.

Shown below are cross sections of some of Santa's sacks (brown is the sack, unmovable, and variously shaped presents are contained within each sack). Can you slide all of the presents out of each sack?

(Clarification on rules: The brown sack portions are stiff and immovable. The presents can move freely within empty space, but at no point can overlap with another present. Santa doesn't delivered squashed presents!)

 

SACK 1

enter image description here

Note from Santa: I was under the impression that we were using these newfangled sacks for space efficiency, but the elves have gone ahead and packed some with empty space inside! I can never trust those little fiends.

 

SACK 2

enter image description here

Note from Santa: This sack is of low quality and has some extra holes, as you can see. I'm mildly suspicious that the elves made those holes themselves... I don't think the presents are removable without using them.
Oh well, at least this sack is fully packed.

 

SACK 3

enter image description here

Note from Santa: When I was unpacking this sack, I had just about HAD it with the elves! I managed to take everything out apart from the red present, which I'm sure you can see is impossible to take out. I complained about this to the elves, and they soaked the sack in fabric softener to get the red present out - and it was a fresh new red coat for me!
Despite all their intrusive, inconvenient, inane and immature pranks, the elves are always good at heart... despite putting my present delivery off schedule by 3 days.

Note from TheGreatEscaper: Merry Belated Christmas and a Happy Be-Earlied New Year!!!

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  • $\begingroup$ Can presents be rotated? If so, what space is required around them to permit it? $\endgroup$
    – Rubio ♦
    Commented Dec 27, 2016 at 8:57
  • $\begingroup$ @Rubio rotation is fair game if you can do it with physical pieces. I designed and tested these with Livecube :) So there may be mild mathematical imperfections, but everything was quite comfortable with my pieces. $\endgroup$
    – TheGreatEscaper
    Commented Dec 27, 2016 at 9:00

2 Answers 2

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Sacks 2 & 3

Firstly, since I did this using a grid and its hard to rotate the diagrams, they've been rotated 45 degrees.

Sack 2

Slide yellow out, then green across. Place purple in the gap so that it touches green and blue. Now slide red across.
enter image description here
Slide light blue up, and purple into the gap as shown. enter image description here
Red across, green up then purple out. Now you move everything back to what it looks like in the image except purple isn't there anymore. Rotate blue then slide it out. Slide red across then rotate to get it out.
Edit: You can't rotate blue at that position. So slide red across, green up.
enter image description here
Now it's possible to rotate blue. Also for red, halfway through rotating (after 45-ish degrees) move green up to provide room to finish rotating red.

Sack 3

Start with red across, then yellow up, purple across and green down. Move blue up and yellow across then purple and green up.
enter image description here
Now you can rotate blue! Do that, and put it in the far top right. Now you can rotate purple! Do that and put it next to blue. Surprise, surprise - now rotate green. Put that in the bottom left.
enter image description here
Slide yellow one left, then move blue down and purple right. enter image description here
Move red across, green up, yellow across, blue across and purple down. Then red across and green can escape!

It's quite trivial to get everything else out as all moves are reversible so in the worst case scenario move everything back to the beginning and then put purple where green was.

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    $\begingroup$ Nice! Welcome to puzzling, Wen ;) I have a bit of an issue with your solution for sack 2; blue can't quite be rotated in the manner you describe. There's also a bit of a hiccup with rotating the big L shapes at the end of 2, but I'm willing to let that one go as it's sort of a subtle detail. Hope you get the rep you need to bulk up this answer :) $\endgroup$
    – TheGreatEscaper
    Commented Dec 27, 2016 at 12:56
  • $\begingroup$ @TheGreatEscaper The subtle detail is that after red rotates about 45-ish degrees, we need to move green up before red can finish rotating. Then red just leaves through the top-right. As for blue, I have no idea... $\endgroup$
    – Wen1now
    Commented Dec 27, 2016 at 23:58
  • $\begingroup$ All the edits are good now :) $\endgroup$
    – TheGreatEscaper
    Commented Dec 28, 2016 at 1:30
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Partial Answer

Sack 1:

Yellow SW; Blue SW; Green NW; Purple NE; Red NE; Yellow SE; Blue SW; Green NW; Green NE and out.
Blue fully NE; then NW; then NE and out.
Yellow NW; then fully NE; then NW and out.
Red fully NW; then fully NE; then NW and out.
Purple fully NW; then NE and out.

for the rest I need some blocks or something that I don't have handy. :(

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  • $\begingroup$ Quick :) Just remember that for the rest of the sacks you'll need to give directions on how to remove more pieces after the first - it's trivial for this sack so it's okay to stop at the first removal, but it's definitely not trivial for the others! $\endgroup$
    – TheGreatEscaper
    Commented Dec 27, 2016 at 8:40
  • $\begingroup$ Just added the rest. :) $\endgroup$
    – Rubio ♦
    Commented Dec 27, 2016 at 8:40

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