### Number puzzle

A co-worker gave this to me today:

What's the next number in this sequence?

0, 1, 2, 720!

A co-worker gave this to me today:

What's the next number in this sequence?

0, 1, 2, 720!

This one's a day late due to flaky DSL...

I'm not even close to finishing this one as it's terribly difficult and I do have a job, but it looks pretty nice when it's all together. To keep with my policy of not posting solutions, I'm going to have to leave out Susanne's nice photo of the completed puzzle, as that is, effectively, the solution. You get the idea, though, right?

The puzzlemaker for this heart has a website, where you can find this as well as yin-yangs, huge rectangles, human heads, and other variations. The maker claims each to be "unique" in that no two are cut the same.

This is a puzzle made up of several interlocking pieces that you have to slide back and forth in order to release them. It's fairly clever as much of the interlocking is hidden in the interior of the puzzle, enough brute forcing you can get the puzzle apart -- my first time around I went a bit overboard and ended up breaking it, which I guess is one possible, but less ideal, solution. It's clever enough that I haven't attempted reassembling it -- disassembling was enough for me.

You can find out more information about this puzzle online, but it's unclear whether or not you can order it online. A photo of the some of the pieces slid out is in the extended entry.

This is my favorite puzzle. It disassembles into individual planks with various triangular configurations on either end. The first time I put it together I had to laid out the pieces in order of disassembly and was able to get it back together. Putting it together without any order information was doable, but took a lot of painful backtracking. You can see the puzzle disassembled in the full entry.

I'm going to be posting several wood puzzle entries as my co-worker Susanne has been bringing them to work. It way my hope to be able to link to some of these so that people could get their own, but these all come from shops in Germany so this appears a bit difficult. Potty Puzzles has a listing of Trench Puzzles that they sell, though they don't appear to sell this one, and they don't include images of the puzzle either -- purchase at your own risk, though you may be able to find a picture of individual puzzles here.

Continue reading "Another wood cube puzzle: Trench's Triple Triangles" »

Susanne has been giving me various evil wood block puzzles to solve. This one is cleverly constructed and scores a medium evilness rating as persistence will get you to the final solution, but you have to backtrack multiple times the first time through. It's disheartening while backtracking to see pieces that were once together and realize that you don't remember how to put them back together.

This post on Kakutani's theorem broke my brain for a bit:

Take two pieces of 8*11 paper and lay them on top of one another so that every point on the top paper corresponds with a point on the bottom paper. Now crumple the top piece of paper in anyway that you wish and place it back on top. B's theorem tells us that there must be a point which has not moved, i.e. which lies exactly above the same point that it did initially.

I feel in a puzzle-giving mood, so here's one that rcp will recognize this from her Oracle interview:

There are 25 horses, and you can race 5 of them at a time. Strangely, you have no stopwatch, but the horses always run exactly the same in every race. How many races does it take to figure out:

* the fastest horse?

* the top three fastest?

For those stumped or wanting to check their answers, read on to see the solution to Friday's coin puzzle.

Here's a puzzle to waste your weekend on. Got it from toons.

Professor S.F. Mann has just returned home, surprisingly unscathed, from a lecture in New Haven. He realizes that he has collected 100 Sacagawea dollars in change from the train ticket vending machines. He tells his kids Billy and Mary that he'll split some of the coins with them. He goes in to his dark room alone and places the coins on a table with 60 of them heads-up. S.F. then tells Billy that he must arrange the coins into two piles without the aid of any light. Afterwards Mary will be allowed to choose which pile is hers and which is Billy's. The children will then receive all of the Sacagawea coins that are heads-up in their respective piles, and S.F. will take the remaining coins. Billy hates losing to Mary and so his goal is to divide the coins up so that each pile contains the same number of heads. He is allowed to shuffle and flip the coins whichever way he wants, but he cannot tell which side is heads up while he is putting them into two piles (the room is dark, and Billy's sense of touch is a bit dim too). What should he do?

I'll post an answer next week, but for now I will state the following:

- Billy cannot stand the coins on edge

- Billy cannot walk away with any coins

- The solution for this problem works all of the time (i.e. the solution does not rely on probability over time)

I'm going to do something useful for you. I'm going to post a puzzle that can get you a job at Google if you solve it. No guarantees, but they'll probably think your smart or something. The puzzle was printed in an ad in the *Tech Review*, though there may be other dorky magazines carrying it.

You have to guess the number that goes on the last column. To get the job you have to e-mail your resume to labjobs@google.com.

(click for larger size)

No posting of answers, though hints are welcome. I don't know the solution, though I've narrowed it down to the candidate solutions.

In case you can't read the columns well, the numbers are 26, 14, 5, 2, 20, and ?.

**Update**: I have seen multiple people suggest in sites linking to this page that the number 20 is in the wrong place. While there may be multiple solutions, including ones that involve moving the 20, I know of a solution that works very gracefully with the numbers pictures exactly as they are in the photo. It's all a matter of *how* you count, and that will be my only hint on this problem.

Hmmm, it took me about a dozen tries before I got this. Supposedly, the smarter you are, the longer it takes. I wish it took me more guesses.

This book is targeted at people who are preparing for an interview. Although it is a book about interview puzzles, the puzzles take up very little of the book. Most of the book is dedicated to interview guides (for the interviewer and interviewee) and the history of the logic puzzle, from its use in IQ tests to its adoption by job interviews. The history was a little bit interesting to me, mostly because it talked about Shockley, and it also happened to mention Jim Gibbons name, which made my world a little bit smaller. The main reason I picked this book up, though, is that I happen to like the puzzles that they give you during interviews, and I'm too lazy to find them on the Internet.

There are plenty of Fermi estimation questions in the book (the title of the book ends up being one). Fermi estimation questions ask you to estimate the value of something you don't know, like the number of redheads in Ireland. When I was in high school, we had an entire unit on this in chemistry. My chemistry teacher introduced the unit by telling the anecdote of Fermi at one of the nuclear bomb tests. As the shockwave approached, Fermi threw some scraps of paper into the air and watched their deflection. From this observation, he came up with an estimate of the megatons of the explosion that was reasonably accurate.

It's really not much use searching for examples of Fermi type problems; pretty much any type of estimation will serve as practice. Although it's nice to have estimation skills, as puzzles I find these a bit boring.

Another class of problems they have are design-type questions, where you get asked how you would design/build some sort of item. While I think these are good interview questions, as they allow the interviewer and interviewee to interact back and forth, I don't find them too interesting to solve in my freetime.

The last class of problems, logic problems with actual solutions, are the ones that I was shooting for when I got the book. There are some good ones in this book which made it worth the price of admission. Here are some of my favorites:

- 5 pirates have 100 gold coins to divide. The senior pirate proposes how to divide the coins, and the pirates then get to vote. If at least half of the pirates agree to the proposal, the division is made; otherwise the senior pirate is killed and the process is repeated. If you are the senior pirate (pirate #5), what should you propose?

- There is a village of 50 husband and wife couples. All of the husbands have been unfaithful. The wives know when men other than their own husbands have cheated, but they don't know about their own husbands fidelity. If a wife can prove that her husband has cheated, then she is required by law to kill him. Also, all of the wives are blessed with Spock-like logic skills. One day, the queen stops by and announces, "at least one of your husbands has been unfaithful." What happens?

- How many points are there on the globe where, by walking one mile south, one mile east, and one mile north, you reach the place where you started?

- Count in base negative 2 (doesn't have a "correct" solution)

- You have five jars of pills. Normal pills weight 10 grams, while poisonous pills weight 9 grams. One of the jars is filled with poisonous pills. Measuring once on a scale, how do you find the poison jar?

I'm only posting this b/c I got it on my first try with the minimum number of moves, and I like to brag:

No-Off by Nob Yoshigahara

(via *BoingBoing*)

I was digging through my archives and found this is one that a nice girl named leahbraids gave me in 1997. It goes as follows:

one four three +three ------- ELEVENYou should be able to replace the letters such that the statement is also true numerically.

Puzzle for you: Michael Gartenberg's Amazing Puzzle

I received this via e-mail by way of Wade awhile back. If you feel like taking a short four question quiz, click on through.

Had this puzzle to keep me entertained awhile back: changing one letter at a time, with every new word being a valid word (e.g. "pail" to "bail"), what's the minimum number of steps to change "WHITE" to "BLACK"? The answer I came up with is below (eight steps).

Mr. Au posed this question today at brunch: is there any *cooked* food that doesn't have its flavor enhanced by adding butter?

This question is harder than it seems. The only thing I've been able to come up with is dry ribs.

Original puzzle:

BUFFYPHILIA

Buffyphilia solved (well, almost):

"HUNDRED SEAPORT BLVD REDWOOD CITY"

One word unsolved: "TEN EFFS" or "STEFFEN"

(*the 'S' should have been an 'I', giving FIFTEEN*)

Description of puzzle: seven pages of screen captures of Buffy and Gilmore Girl episodes. On each page the screen captures are arranged in a cross. The first page serves as a link to each of the other pages. On the other pages, it is noticeable that the sizes of the images don't line up perfectly, this turns out to be the key to the puzzle (it turns out that the names of the episodes is not meaningful). The other key to the puzzle is to ignore Gilmore Girl episodes. The baseline dimension of the images is 240x180. The encoded character is determined by the offset from that size, so 241x180 = A, as does 240x181.

X - Gilmore Girls episode, ignore

Index 0: establishes baseline for character decoding

240 180

240 180

240 180

240 180

240 180

240 180

Index 1

BLVD (If you include Gilmore Girls, you get BEDEVIL, clever)

244 180 D

240 182 B

240 202 V

252 180 L

X 240 185 E

X 245 180 E

X 249 180 I

Index 2

FIFTEEN (originally decoded wrong as TEN EFFS/STEFFEN)

240 185 E

240 186 F

240 186 F

240 185 E

260 180 T

254 180 N

249 180 S (This should be an 'I')

Index 3

CITY

240 183 C

240 200 T

249 180 I

265 180 Y

x 248 180 H

x 240 199 S

x 258 180 R

Index 4

HUNDRED

254 180 N

240 185 E

240 184 D

240 188 H

261 180 U

258 180 R

244 180 D

Index 5

SEAPORT

260 180 T

240 181 A

240 185 E

240 196 P

258 180 R

255 180 O

259 180 S

Index 6

REDWOOD

258 180 R

240 195 O

240 195 O

240 184 D

263 180 W

244 180 D

245 180 E

Here is another clue that we got from their Web site. We had to listen to a bunch of sound clips, identify the movie, and then pull out the clue:

THIS IS NOT A PRECLUE IT IS TIME DATA

2002 10 19

10a [TOPGUN] Good morning gentlemen the temperature is 110 degress... Holy Shit it's Viper

11 [HAPPY GILMORE] Checkout the nametag, you're in my world now Grandma

12p [IJ: LAST CRUSADE] My boy, we are pilgrams in an unholy land

1 [Star Trek VI] Course setting captain? Second star to the right, and straight on til morning

2 [IN THE LINE OF FIRE] What do you see when you're in the dark and the demons come?

3 [STAR WARS: A NEW HOPE] Your eyes can deceive you, don't trust them

4 [NOTHING TO LOSE] I can't feel my ass... I didn't know an ass could fall asleep, it's all tingly and shit

5 [OFFICE SPACE] I can't believe what a bunch of nerds we are. We're looking up money laundering in a dictionary.

6 [TRON] There's a 68.71% chance you're right

7 [ANIMAL HOUSE] I gotta work on my game. Nah, don't think of it as work, the whole point of it is to just enjoy yourself

8 [PRINCESS BRIDE] Inconceivable!

9 [RAIDERS OF THE LOST ARK] Snakes, why did it have to be snakes... very dangerous, you go first.

10 [ENEMY OF THE STATE] Conspiracy theorists of the world unite. Well it's more of a theory. I'm a former conspirer

11 [CLUE] Are you a cop? No, I'm a plant? A plant? I thought men like you were called a fruit

12 a [LITTLE SHOP OF HORRORS] feed me now, I'm starving

1 [UNFORGIVEN] well i guess i had it coming. "we all have it coming kid

2 [EVIL DEAD] (weird incantation)

3 [INNER SPACE] when things are at there darkest pal it's a brave man who can kick back and party

4 [THIRTEENTH FLOOR] They say ignorance is bliss. For the first time in my life I agree. I wish I never encountered the awful truth voice

5 [IJ: TEMPLE OF DOOM] I hate the water, I hate being wet, and I hate you

6 [SOUTH PARK] You better get packing bitch

7 [TRUMAN SHOW] "good morning, good afternoon, good evening,

and good night")

8 [INDEPENDENCE DAY] "using one signal to synchronize their efforts.... in 6 hours checkmate"

9 [Matrix] "morpheus!"

10 [EARTH GIRLS ARE EASY] what did you say? oh nothing, I'm on drugs

11 [DIRTY HARRY/THE MASK] (do I feel lucky... well do you punk?)

12 p [ARMAGEDDON] after this is over, can I like get a hug from you or something?

1 [TOY STORY] I don't like confrontations!

2 [ALIENS] Game over man, game over

We received the letter clue from the game. The one was pretty easy. The clue is encoded in the -ly adverbs, which stand out because they seem very out of place. The extracted adverbs are:

unilaterally

rapidly

literally

presently

lately

uniquely

slyly

pragmatically

healthfully

outrageously

deliberately

rapidly

obviously

magnanimously

accordingly

Which gives the clue: "url plus phodroma"

- fobik.org/phodroma

Plain text of letter is in the extended entry.

- The Game: Letter
- The Game: Another preclue
- Puzzle: The Game: Buffyphilia
- Puzzle: Butter
- Puzzle: WHITE->BLACK
- Puzzle: Think you're smart
- Puzzle: E, N, Y
- Puzzle: ELEVEN
- Tile puzzle
- Book: How Would You Move Mount Fuji
- Petals Around the Roses
- Puzzle to waste your weekend
- Coin puzzle
- Answer to Coin Puzzle
- Puzzle: Horsies
- Kakutani's theorem
- 3D Jigsaw puzzle
- Another wood cube puzzle: Trench's Triple Triangles
- Burr puzzle: TB Blues
- Jigsaw puzzle for Valentine's Day
- Number puzzle