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Showing posts with label Puzzles. Show all posts
Showing posts with label Puzzles. Show all posts

Monday, July 8, 2024

High Five Wire Puzzle


Without magnets and glue, how can they be combined?
UINVEA

I've seen bunches of puzzle videos, but this is the first one that really grabbed me. Grabbed me so much I went looking for it. Constantin makes it, and Knobelbox is the only place where I found it, and they are out of stock. There is a four wire version as well.

Sunday, December 10, 2023

Machinist Puzzle


Free the Nut! (Not What You Think)
Inheritance Machining

Guy using a lathe and a milling machine to make a captive nut puzzle. Unlike some machining videos, this one moves along at a steady pace, no long shots of turning or milling a part, just short clips that are just long enough for you to get the gist of what he's doing. Plus it's a puzzle for the viewer. He shows you all the pieces, so you might be able to figure out how it works.

Wednesday, May 18, 2022

Jack


2015 To 2019 GM Chevrolet Colorado Truck - Bottle Floor Jack Location Behind Seats
Paul79UF

I have been meaning to go over to diabolical daughter's house for, what, a couple of weeks? ever since we had the big dumpster event / pizza party and pick up the wheel chocks for my truck. Yesterday I was pleasantly surprised to notice that the chocks were sitting in the back seat of my truck.

My mission for today was to put the jack and wheel chocks back in their place behind the seat. Unfortunately I couldn't figure out how they all fit together. YouTube to the rescue. It's kind of weird because the base of the jack has four little holes, two of which are designed to sit over little tabs in the storage space. However, if you are not careful with stowing the chocks, they will cover the holes and the jack won't fit in its place.

Anyway, thanks to whoever put the chocks and pieces back in my truck.

And for those of you who thought this message was going to be about my friend Jack, I looked up Jack in the owner's manual and it directed me to the page about the stereo input jack.

Thursday, May 5, 2022

Wordle

I play Wordle most every day, it's just my speed. Some days the answer appears as if by magic, other days I am wrought with anguish. Today's puzzle was super-annoying. On my second guess I got three of the letters in the right place. Do you know how many words there are with the letters placed like this:

_ O _ E R (highlight to read)

I thought of nine right off the bat, and I've only got four places left to use. Well, what I need is a word made entirely of letters that haven't been used yet, but that doesn't help much. I've still got 16 letters to choose from, I may as well be starting blind. If I am lucky, sticking in some random word would help, but would it be enough help to be worth one of the four places I have left? I decided it wasn't and instead tried to eliminate as many words as I could from my list. Two words had a B and two words had an N, so with two guesses I was able to eliminate four words from my list. It wasn't enough. The answer was the name of a fictional TV persona. 

(H O M E R) (highlight to read) 

It was on my list, but I had discounted just because of the name association. Too late I realized it also referred to a baseball play, and it's spring, and all right thinking people's thoughts turn to baseball. If you're not thinking about baseball, that makes you some kind of commie. Wasn't that the standard test of suspicious persons during WW2 and the Cold War? Guess I flubbed that test.


Sunday, January 16, 2022

GANCUBE

 

Megaminx

Got an email from GANCUBE promoting their line of Rubik's Cube puzzles. I thought they were a fad that faded away a while back, but evidently it's still going strong. These guys seem to have a near endless variety of these things. I've played with them a few times and I think I even solved one, once. I don't know why, but they never really grabbed my attention. They're cute and all, but what do you get when you solve it? The same thing you started with. And is the 'solution' any more valid than any other combination? I know most puzzles / games are the same way. Maybe they were too much work, maybe I'm not as smart as I think I am.


Sunday, November 14, 2021

Jumble Does Pulp Fiction

Sunday Jumble

Does this scene look familiar? Yeah, maybe, just a bit.

Vincent Vega (John Travolta) & Jules Winnfield (Samuel L. Jackson)

If you want to see the puzzle, you have to go buy a copy of a Sunday paper. I've already scribbled all over mine. There is an online version of Jumble, but until recently it only carried the daily puzzles, not the more challenging Sunday version. I don't like the online version of the daily puzzle, there are too many clues available, which means it is not as challenging. I haven't tried the Sunday version yet, and as long as I have a paper version available, I'll probably stick with that.


Monday, August 9, 2021

Square Cross Puzzle


How did Ramanujan solve the STRAND puzzle?
Mathologer

I started watching this video the yesterday. I got as far as the square cross puzzle (timestamp 1:45 to 2:20), and that intrigued me. I stewed on it overnight and this morning I came up with this analysis.

Square Cross Problem

We start with a drawing of a cross. The cross is composed of five squares. The center of the cross is a square. Attached to each side of the central square is another square of the same size.

Our mission, should we choose to accept it, is to cut the cross into five pieces and then reassemble those pieces into two crosses with the same shape. These two new crosses are the same size as each other.

Since we are making two crosses from the original larger cross, each of the smaller crosses must be one half of the area of the original larger cross.

If the length of the side of one of the component squares of the larger cross is one, a little algebra will show us the the length of the side of one of the component squares of the smaller crosses must by the (2^0.5)/2 (the square root of two divided by two).

Cutting each of the component squares of the original square on both diagonals will give us 20 right isosceles triangles. Two of those triangles joined together along their hypotenuse will give us a square the same size as one of the component squares of the smaller crosses. Two triangles for each of five squares requires ten triangles to make one smaller cross. Two times ten is twenty, the number of triangles we got by cutting up the larger cross.

This is the brute force method. It shows we can cut up the larger cross into smaller pieces and reassemble them into two, smaller, crosses. However, we have twenty pieces, not five, so we do not have a solution to the stated problem.

The trick is to find cuts that do not need to be made so that when we cut up the larger square we only have five pieces. Now I'm thinking a computer program could make short work of this if I can just figure out how to encode it.


Saturday, August 7, 2021

Number Jigsaw Puzzle

Completed Puzzle

Dennis gave me this puzzle for my birthday. I spent a few minutes trying to solve it but then realized I could write a computer program to solve it, much like I did for another puzzle he gave me.

It didn't take long to write it, but it took a while to track down the bugs and to polish it up a bit.

Puzzle Pieces

The first problem was how to represent the puzzle pieces in the program. With the cube puzzle, I was able to use a 64-bit integer to represent the 4 x 4 x 4 cube. This puzzle was a little trickier.

Seven Segment Display

The digits here are modeled on the seven segment displays that are common in simple electronic devices. Note that each segment is shaped like a rectangle with a triangular point on each end. If the puzzle pieces closely followed the electronic pattern it would have been simple to encode them as data. However, some of the pieces, like the zero, one and seven, included a bit that isn't part of the original pattern, and some (the zero) were missing a bit. 

Zero

I decided to 'draw' the digits using ASCII characters. Each true segment was represented by three characters. I couldn't come up with a good visual method of representing multiple triangles in one space, so I gave each segment three full spaces and left a space between segments. 

Playing Field

The playing field, like the individual digits, is an array of character strings. Valid places are marked by vertical bars or hyphens. Invalid places are marked with X's and spaces.

Most of the mechanics of the program were pretty straight forward and didn't give me any trouble, but I tried to use a minimal amount of space for the puzzle pieces and that kept biting me. Eventually I realized I needed an extra row of spaces surrounding each character and around the playing field as well and then things started coming together. (It's not that I was trying to save space, 200 bytes isn't going to make any difference in a machine with gigabytes of RAM. I was trying to adhere to the old dictum of 'necessary and sufficient'.)

I let it run for a while and it found multiple solutions, but after a 20 odd hours I said this is enough, shut it down and started looked at just how many combinations I was testing. Pieces can be rotated through four different orientations and can be flipped to make a mirror image. Not all pieces need all four rotations. Turn some pieces (like the two) 180 degrees, and you are back where you started. And for some, the mirror image is identical to the original. So I modified the program to use this information. Now it runs to completion in just over an hour and found 16 possible solutions.

Every solution required at least one piece to be flipped to become its mirror image.

Digit:       0 1 2 3 4 5 6 7 8 9
Solution  1: 0 0 0 0 0 0 0 1 0 0
Solution  2: 0 0 0 0 0 0 0 1 0 0
Solution  3: 0 0 1 0 0 1 0 1 0 0
Solution  4: 0 0 1 0 0 1 0 1 0 0
Solution  5: 1 0 1 0 0 0 0 0 0 0
Solution  6: 1 0 1 0 0 0 0 0 0 0
Solution  7: 1 0 1 0 0 0 0 0 0 0
Solution  8: 1 0 1 0 0 0 0 0 0 0
Solution  9: 1 0 1 0 0 0 0 0 0 0
Solution 10: 1 0 1 0 0 0 0 0 0 0
Solution 11: 1 0 1 0 0 0 0 0 0 0
Solution 12: 1 0 1 0 0 0 0 0 0 0
Solution 13: 1 0 0 0 1 0 1 0 0 1
Solution 14: 1 0 0 0 1 0 1 0 0 1
Solution 15: 1 0 1 0 1 1 1 0 0 1
Solution 16: 1 0 1 0 1 1 1 0 0 1

Table showing which digits were flipped

For pieces in a vertical orientation, there are 15 possible positions on the playing field. Pieces lying on their sides have 16 possible positions. Zero is a special case as it is the first piece we play. Any position past the halfway mark can be considered a mirror image of the playing field and so we only have 10 possible positions for the zero (6 in vertical orientation and 4 in horizontal).

This gives a total of 4.3 times 10 to the 18th power possible placements. The program tried approximately 450 million combinations on its way to finding the 16 solutions.


Sunday, March 14, 2021

Dr. Seuss

Today's Jumble

Today's Jumble features Dr. Seuss. Don't suppose their choice of topic has anything to do with the kerfuffle going on in the idiot sphere, do you?

Yes, I was able to unscramble the six words, but the phrase at the end has me stumped. The letters that need to be unscrambled are:

E E I I O F F H H L M P R S Y

I put the vowels first and then the consonants, both in alphabetical order. Sometimes it helps.

Tuesday, February 16, 2021

Soong Mei-Ling

1943 Soong May-ling in White House Oval Office gave a press conference.

The clue for today's Jumble is "Eric Gugler’s 1933 Oval Office redesign was underway and things were —". Seems the oval office was an FDR thing. Here I thought it had been there forever. I go looking for pictures and I am not finding much, and then I trip over this one. Since China seems to be feeling their oats, building all kinds of infrastructure all over the 3rd world, stomping on personal freedom in Hong Kong, and pushing everyone else out of the South China Sea, this photo makes me think it might be time to pause and reflect on how we got here. It wasn't pretty. 

Sunday, October 25, 2020

Cube Puzzle Solver Port-Mortem

Number of times search was blocked by level.

I modified my cube solver program to keep track of the number of times a search at each level failed. There are ten pieces to the puzzle, so we search at ten different levels, one level for each piece. The graph shows the number of times the search of all possible positions at that level did not find a single one that could hold the selected piece.

Levels 0 thru 4 don't even register above the X axis at this scale. Including them made the key confusing, there wasn't enough differentiation in the colors, so I didn't include them. Level 5 shows a flat line even though it has counts consistently above 10 billion (10^10). I included it just to give you an idea of the scale we are working with.

The program printed this data to stderr, which by default goes to the terminal screen. Copy and paste that into the text editor and then replace all instances of multiple spaces with a single tab. (Start with the longest sequence of spaces you can find and then work backwards.) The formatting is lost, but now you can copy and paste that into a spreadsheet and our formatting is restored.

I did some calculations in the spreadsheet to see how many comparison tests we avoided and came up with about 4.5 quadrillion, which is a very large number, but still nowhere near the value of 

12 * (3*96)^4 * (4*96)^5 = 6.8929848e+23

which is what I expected. So there is something wrong with my calculations somewhere.

P.S. Something weird happened when I pasted the text into the spreadsheet. I got a bunch of lines consisting of the single word #ERROR! I looked in my source code, but couldn't find it, and I just looked in the text file and it's not there either, so I think Google Sheets must have found something it didn't like (like a line of 300 periods) and complained. No problem, simple sort the file and all the ugly stuff you aren't interested in gets lumped together and can easily to erased.

P.P.S. One trick I use when dealing with large quantities of data is to insert a column along the left hand edge, a new column A if you will, and then number all of the lines with sequential numbers. You can easily do this by typing 1 in box A1, and then =A1+1 in box A2. Copy box A2, select all the rest of column A from A3 to the end paste. Now all the lines are numbered sequentially. However, you are not quite done. If you sort the sheet now, all the values in column A will be recomputed and your original order will be lost. So what you do is copy column A and the Paste Special -> Values Only back over it. Now you have an indelible original order. Sort however you like, but you can restore the original order by sorting on Column A.


Sunday, October 18, 2020

Cube Puzzle Part 2

Recursion

I modified the program so it now finds all 335 solutions. It runs quite a bit longer now, almost 15 hours. I also uploaded a text file that illustrates all how all the transformations are done to place a piece in the cube.

The program made 41 billion comparisons, which is a bunch, but a far cry from the umpteen zillion I expected. Since the 10th root of 41 billion is only about 11, I'm thinking most searches must have reached the end of their list early on.

The program starts with the first piece placed in one of it's twelve possible positions. The first piece has only 12 possible positions as all of the other positions (276) are simply rotations of one kind or another.

We are going to test each of these against all 288 possible positions for the 2nd piece. Some of these tests will fail, indicating the pieces would collide, but most will pass. Of those that pass, we will test all 288 positions for the 3rd piece. More tests will fail at this level and fewer will pass. There will be 335 searches that will go through all of possible positions at all levels, but that only amounts to 

(12 + (3*96)*4 + (4*96)*5) = 3084

I suppose I could track how deep each search goes and perhaps a graph of the averages might give some insight, but I expect it's some kind of exponential curve. Besides, I got my solution, put the puzzle together and shipped it off to my niece. We shall see what she does with it.

Part 1 here.

Saturday, October 3, 2020

Cube Puzzle

Cube Puzzle

Dennis made this puzzle. It got taken apart a while back and I never mustered the drive to put it back together, but now I want to send it to my niece, so I really should put it together so she knows it can be solved. I don't know how long solving it by hand would take, but it should be a simple matter to write a computer program to solve it, and it was. Took me a few hours over the last couple of days.

Fitting together pieces of the Cube Puzzle

I don't know how long solving it by hand would take, but it should be a simple matter to write a computer program to solve it. I started working on a program to solve it earlier this week. I am not sure a brute force program can solve it in a reasonable amount of time.

Schematic representation of puzzle pieces

There are ten pieces. All pieces are one unit thick. There are five pieces with gross outer dimensions of 2 x 4 and five pieces that are 3 x 3.

In a single plane:

  • A piece can rotated to any of 4 orientations.
  • A piece can be flipped upside down, so there are 2 situations.

A piece can be in any of the 4 planes. 

The cube can be sliced into four planes and this can be done 3 ways:

  • horizontally
  • vertically
  • orthogonal to the other two

Multiply those together (4 x 2 x 4 x 3) and we have 96 possibilities.

In a single plane, using a single orientation, just sliding the piece around in the 4 x 4 space:

  • A 2 x 4 piece can have 3 positions. 
  • A 3 x 3 piece can have 4 positions.

In sum:

  • The (5) 2 x 2 pieces have 3 x 96 possible positions.
  • The (5) 3 x 3 pieces have 4 x 96 possible positions.

Combining all these we have (3*96)^5 x (4*96)^5 or 1.6543163e+25.

I think. I may have it all backwards.

If that is the correct value, it is doubtful whether a brute force program will be able to solve the puzzle. I'm guesstimating it will take a billion years. On the other hand, many possibilities will fail almost immediately. At this point I was wondering whether it is worth going ahead with writing the program.

Cube Puzzle Solved

The lure of solving an unsolvable problem was too great and I went ahead with the program. It only took a few hours over a couple of days to write and after 7 or 8 minutes of execution time, it came up with a solution that actually worked.

Solution

With some embellishments, I was able to have it run through all the possible permutations and it delivered an even dozen solutions. It only took 42 minutes to deliver these answers, not a billion years, so something is not right.

Faced with this dilemma, I find it sometimes helps to explain the situation in English, so here is an exposition of the mechanics of the program. Hopefully, it is not too technical.

The cube is 4 units on a side, so there are 64 (4 x 4 x 4) positions. Each position is represented by a bit in 64-bit computer word. A single piece's position in the cube is represented by setting the appropriate bits in a word. A set of nested loops iterates through all the possible permutations (enumerated above) and a set of procedures translates the pattern of the piece in question into it's location in the cube.

We start by generating a word for each possible position for each piece. This doesn't take long, less than a millisecond, as there are only 672 of these ((4 x 96) + (3 x 96)). Each of these words is treated as a bit mask. If you AND two of these together and the result is zero, then there is no interference, so those two pieces, in those positions may coexist in the cube. If the result is not zero, then the pieces interfere with each other and this combination cannot be part of the solution.

If the result is zero, then these two masks can be OR'd together to give us a new mask. We can then proceed to the next piece and iterate through all the masks until we find one that does not interfere. If we cannot find such a piece, we go back to the previous piece and try the next position.

Now it could be that many of the positions are excluded early on, so that we only end up actually having to test a small fraction of the possible combinations. Still, it makes me wonder if I am missing something fundamental. Sometimes Lady Luck does shine on us, but this doesn't seem like this is one of those situations. I spent some time working on program to solve the Eternity II Puzzle, and that kind of persuaded me of the futility of applying brute force tactics against insurmountable odds.

Source code here.

P.S. In the course of writing this, I realized that there may be more solutions that my program did not uncover. As soon as I found one solution, I went back to beginning and went to next mask for the first piece. Perhaps I will rectify this shortcoming. Someday. Maybe.


Thursday, October 25, 2018

Pipe Organ Desk

Pipe Organ Desk
Kagen Sound built this desk for Darren Aronofsky, the film director. There is a small pipe organ built into this desk, but it is not there to make music, it is part of a complex mechanism to unlock a secret compartment. It's really quite spectacular. The entire desk is riddled with complex puzzles. There are several videos on YouTube that show how some of it works. I didn't find them particularly engaging.

Via older son.

Thursday, October 20, 2016

Cubic Trisection Puzzle


Cubic Trisection

You can easily make three identical pieces that can be put together to make a cube. Simply take six flat squares, group into three pairs and join the two squares of each pair at right angle. You can then assemble the three right angles into a cube. But they won't stay together. If you just set it down and don't touch it, it might hold together, but jostle it and it will collapse. This cubic trisection is a little peculiar. Make that very peculiar.

This puzzle was invented by Robert Reid. Doesn't seem to be much information about him, possibly since he spent 50 years running a cinema in Peru.

Via Dennis.

Sunday, April 3, 2011

Alphabetical Order

When I am working a Jumble puzzle, after I have unscrambled the initial set of words, I will copy the circled letters to a space just below the space for the mystery phrase. I use a one to one order, one circled letter per space in the mystery phrase. This helps to insure that I have all the letters necessary for the phrase, i.e. I'm not missing any, and I don't have too many.

Sometimes the mystery phrase is obvious, and sometimes it's obscure. For the difficult ones I will sometimes recopy this set of letters and put them in alphabetical order. Today's puzzle was obscure, it was also really long, much longer than normal. So I thought I would make this alphabetical copy, and that's when I realized the letters were already in alphabetical order, and, Oh! Look! Alphabetical Order is the solution as well!


The sharp eyed will notice that the letters written into the space for the answer have a much lighter stroke weight than the others. This is because it was done with one of the those rolling writers, just touching the paper. They work just like ball pens when you use a firm pressure, but they will also write even if they are just barely touching the paper at all. Notice the tails on some of the letters in the initial set of words. Those happen when I lift off the paper while the pen is still in motion. I suspect I used a lighter pressure when I was writing the final answer because I was writing a long series of letters, and it saved time and/or motion. Using a heavier pressure would have involved pushing the paper down until it stopped, writing the letter, stopping, and then lifting the pen. Using a lighter pressure mean just lowering the pen until it contacted the paper and then writing the letter. Obviously requires a more sensitive touch. Does it save energy? Or does exacting that much control require more energy? Hmmm. Probably have to write a lot more on wavy newsprint to find out.

Update February 2017 replaced missing image.

Thursday, December 17, 2009

Number Puzzle

Marston sent me this puzzle:

If:

2 + 3 = 10

7 + 2 = 63

6 + 5 = 66

8 + 4 = 96

Then:

9 + 7 = ?


The answer is the password to an attached spreadsheet. Figure out the answer, and you can open the spreadsheet and add your name to the list of people who have solved this problem. Only problem is I don't have Microsoft Excel. I do have Open Office, so I can open Excel spreadsheets, and when I try to open this one it does indeed check for a valid password. However, I cannot save it as a protected spreadsheet in any format, so I could not add my name to the list. Some deficiency in Open Office, I suppose. So now I am in a bind. I cannot demonstrate that I can solve the puzzle without giving you the solution. Of course by now this problem and its' solution are all over the net, so if you really wanted to cheat, you could. The problem is not that difficult, so if you enjoy this kind of thing, you might try to solve it. If you want, I can forward the protected spreadsheet to you so you can amuse your friends.

After I used Open Office to convert the spreadsheet to the Open Office format, I was able to upload it to Google Documents, but when I tried that with the protected Excel format version, I got an error.