Plus One Puzzle

[mtairymd]

This is one of my favorite puzzles so far. You are given 8 blocks that must be placed in a box. They will fit and the box will be "totally filled." Once you are done, slide the lid on the top to complete the puzzle. Your test subjects might feel pretty smart by knowing that they solved this puzzle within a few minutes. However, you have a surprise. Pull the extra piece from the lid and tell them to place it in the box. I've tested this puzzle with 20 people so far and the common response is "No Way!". But yep, it can be done.

I've included the basics here but honestly there are too many steps/drawings to recreate.  If you are interested, I've posted full Instructions here:
https://www.instructables.com/id/Plus-One-Puzzle/

This video shows the solution but doesn't answer the why. Do you see a difference?

 

Here are pictures of the finished puzzle.

Showing solution

I start with CAD Drawings.  Detailed drawings are shown in the link above.

I've mentioned on former projects about using scrap wood. Well, someone gave me grief about my seemingly "endless supply" of scrap. Actually, I do have a lot of scrap wood that was donated to me by my boss. He previously owned a custom woodworking shop and couldn't see throwing exotic hardwood scrap in the ol' wood stove. Anyway, I was more than happy to take all the scrap off his hands.

9 Blocks Needed for box

Box Build (1/4" notch)

5 Sides

Glued it together

Lid and EXTRA block

Finished Box and Lid

8 Blocks

9 Blocks

Notice anything different with the dimensions?

8 Blocks stacked

 

These cross-sections give away the secret. The x (4.5") and y (3.0") dimensions stay the same but notice the gap between the blocks and lid goes from 0.122" to 0.031". This is the difference that is hard to see when you are staring at the puzzle.

For a double check, calculate the volume of both stacks and compare them to the added block. Note that you won't get an exact match (V1 + Block5) < V2. I accounted for this in the CAD model by adding small (.005") gaps between a few of the blocks on V2.

All done

That's it.  Please let me know if you have any questions.

 

 

 

 

 

 

 

[gee-dub]

Fun stuff.  I have a puzzler at work.  I may have to gift her one of these.

[mtairymd]

5 hours ago, gee-dub said:

Fun stuff.  I have a puzzler at work.  I may have to gift her one of these.

I was pleasantly surprised with this puzzle.  The look when you tell them that an extra piece needs to fit in the box is pretty funny. 

[Tpt life]

I was a loader for awhile. It was fun on long gig tricks to see who could load the trailer tightest. A “full” trailer at journey’s start was often half full each night after a week. Neat puzzle concept. 

[mtairymd]

3 hours ago, C Shaffer said:

I was a loader for awhile. It was fun on long gig tricks to see who could load the trailer tightest. A “full” trailer at journey’s start was often half full each night after a week. Neat puzzle concept. 

Thanks.  I work in packaging electronics so passing this puzzle around the office was interesting :). 

[wdwerker]

That's pretty neat ! Kinda like Tetris in 3D.

[mtairymd]

1 hour ago, wdwerker said:

That's pretty neat ! Kinda like Tetris in 3D.

Thanks. 

 

[wdwerker]

A version with " L" and "T" shapes would really be neat especially if you could lay your hands on some brightly colored exotics. Paduak, purpleheart, Holly and zebrawood come to mind. Then there are always brightly colored dyes. Highland sells Arti toymakers dyes.

[mtairymd]

2 minutes ago, wdwerker said:

A version with " L" and "T" shapes would really be neat especially if you could lay your hands on some brightly colored exotics. Paduak, purpleheart, Holly and zebrawood come to mind. Then there are always brightly colored dyes. Highland sells Arti toymakers dyes.

I agree.  However, my first try at cutting L & Ts didn't turn out very nice (see pics).  My skills have improved but tight tolerance parts are still challenging for me.     

Nice tip on the dyes.  

[wdwerker]

Inside corners are challenging.  I often cut parts slightly oversized 1/32- 1/64 and sand on a machine like the Ridgid belt/ spindle sander to clean up saw marks and achieve exact sizes desired.  An osselating multi tool can sand inside corners quite well. Calipers help check size faster than squinting at a ruler. 

Using a real good crosscut saw blade greatly reduces the effort needed to clean up end grain.  Softer woods like basswood should  sand and accept dyes easily. 

[mtairymd]

1 hour ago, wdwerker said:

Inside corners are challenging.  I often cut parts slightly oversized 1/32- 1/64 and sand on a machine like the Ridgid belt/ spindle sander to clean up saw marks and achieve exact sizes desired.  An osselating multi tool can sand inside corners quite well. Calipers help check size faster than squinting at a ruler. 

Using a real good crosscut saw blade greatly reduces the effort needed to clean up end grain.  Softer woods like basswood should  sand and accept dyes easily. 

Yeah, I found that out...lol.  A while back, someone sent me a website of a guy that builds the pin and block puzzles.  He uses fixtures and bearing slides to achieve .003" tolerances.  His work looks awesome.  I used a band saw with a drawn on pattern.  Hence, the big gaps :).    

For the box the puzzle, I did cut everything 1/64" oversized and sanded it down with caliper checks.  I'm pretty happy with the fit but it was time consuming.