Introduction: Plus One Puzzle
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.
This video shows the solution but doesn't answer the why. Do you see a difference?
I understand the originator of this style puzzle was a German Puzzle maker by the name of Bernhard Schweitzer and a similar version (smaller & metric units) is sold on Amazon. I spent way more time than I would like to admit working out the dimensions for this version and additional hours in the workshop trying to get the blocks to be within tolerance (hand sanding). If you are a glutton for punishment and/or a better woodworker than me, take a shot at making your own :).
Step 1: Tools/Materials
Step 2: Drawings
You will be building to the CAD drawings. The parts are color coded for easy reference.
Step 3: Blocks 1 - 5
I tried to stick with common fraction sizes for the width and height. The depth worked out to be a unique number. For the first 4 blocks, the depth is 0.636". Block 5 (blue) is similar to block 2 (yellow) except for the hole for the lid pin.
Step 4: Blocks 6 - 9
These blocks are all 1.273" thick. All cuts are made on a table saw.
Step 5: Block Summary
You can use this table as an aid when making the blocks. I suggest printing it and marking off the pieces and cuts while you are working. Note the common sizes (depth) of 1", 1.5", 2", 2.5" and 3". Hint: After setting up your saw, make all the same cuts at once to save time.
Step 6: Block Cuts
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.
As for the cuts, they were pretty straight forward. The puzzle does require tight tolerances so take your time when doing the measurements.
Step 7: Blocks
Here are the finished blocks. I used danish oil on all the pieces for the finish.
Step 8: Fit Check - Thin Layer
This is one option for the layout. The key is the 4.5" x 3.0" dimensions. Note that the box only has clearance of 1/32 of an inch on all sides.
Step 9: Fit Check - Thick Layer
Same check as the 'thin' layer.
Step 10: Fit Check (8 Blocks)
If you did everything correctly, the dimensions should work out as shown when stacked. If not, fine tune the blocks by sanding.
Step 11: Fit Check (9 Blocks)
Notice anything different with the dimensions?
Step 12: Box Drawing
All parts of the box (except for the knob) were made from 1/2" thick poplar.
Step 13: Sides
Cut to the size shown. I used a router/table to cut the notch.
Step 14: Bottom
Simple cut done on the table saw.
Step 15: Back
Used the router table again for this piece. Note that the slot must be wide enough to accept the lid.
Step 16: Front
Another straight forward part.
Step 17: Box Parts
Ready to glue together.
Step 18: Box Assy
Use wood glue and clamps to secure the parts.
Step 19: Lid
Router for the edge cuts. Use a 1/2" Forstner bit for the hole.
This video has nothing to do with the project - just me playing with a slow motion while drilling a hole.
Step 20: Lid Pin
Cut a 1/2" dowel to the length shown. I used a band saw for this cut.
Step 21: Lid Assy
Glue pin into the lid as shown. The blue block is removable so DO NOT glue this joint. This block should have a tight fit onto the pin.
Step 22: Section Cuts
Slide the lid into the notches. Clean up the joints with wood filler and sanding.
Step 23: How Does It Work?
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.
Step 24: Box Pictures
Pictures of the box after adding finishing with oil.
Step 25: Lid Pictures
Lid and Block 5.
Step 26: 8 Block Layers
The first picture is the thick layer. The second picture has the thin layer on top. This is obviously interchangeable. In addition, from the test subjects, I found there are multiple ways to make these 8 blocks fit into the box.
Step 27: More Pictures of 8 Blocks in Box
Step 28: Complete First Phase of Puzzle
These pictures show the 8 blocks placed in the box with the 9th block on the lid.
Step 29: Hard Part Starts Now
Remove the block from the lid and try to fit it in the box. This is the "what the heck moment."
Step 30: Rearrange Blocks
Hopefully the graphics help. If not, refer to the video.
Step 31: Completed Puzzle
Add the lid and you are finished. Thank you for viewing!
Step 32: 3D Print Files Added
I've attached the STL files for those that would like to print the puzzle. Note that you will need to glue the box walls together. If anyone prints it, please post pictures. Thanks!
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Please be positive and constructive.