Puzzle Number 16: Trip to Canada

Raylan is a young boy in Kentucky whose Uncle Olyphant has just returned from a trip to Canada. On the drive home from the airport, Raylan excitedly asked his uncle what he did.

"Well, son," Uncle Olyphant replied, "My first night was spent in a frigidly cold environment with a constant siren warning me to keep watch for polar bears. Needless to say, it was not a very pleasant time. However, my trip quickly got much nicer, as the next day I found a fancy golden dagger, and shortly after that I ran into a beautiful alabaster stallion. I went to a show which ended up being a fascinating musical number performed solely by a fellow's mouth, followed by a few days watching the largest species of European deer roam about the prairies. After that, I found the jaw of the largest deer in the world. The next day, to my surprise, I won a marvellous wooden cylinder which one can stick in the wall and hang a hat on. From there I went on to a recently established collection of stores to see if I could find any souvenirs for my favorite* nephew, but we'll talk about that a little more once we get home. The next thing I did was visit a trio of French rivers. A little farther along, once the river was mostly English again, I had to ford it in a location where it was full of voracious eels. Despite the danger, it was well worth it in order to get to a fascinating bay perfect for cattle. From there I caught a boat in order to go see a wall made entirely of maize, and finally ended the trip by visiting a large community of friendly and well-mannered dogs."

Raylan looked quizzically at his uncle. "That sure sounds like a nonsensical trip, Uncle Olyphant. Where in Canada did you go to do all of these things?"

Uncle Olyphant smiled and said, "Son, I've already told you."

Where did Uncle Olyphant go?

Solutions to the puzzle can be found here.

* Note the authenticity of his American speech with the lack of a 'u'.

Interim Puzzle

I had a number of people tell me they would get back to me with more answers from this past puzzle, so I have decided to provide a brief extension before I post the answers. In the meantime, here is a very cool pictorial puzzle that one of Sarah's friends shared with her called Not to Scale. It is surprisingly fun and challenging.

Puzzle Number 15: The Oblique Title Wars

I realize it has been a long time since I posted my last puzzle. Since the Oblique Title puzzles have always seemed to be a favourite, I figured another installment made the most sense. As a reminder to those who haven't played before, the following is a set of movie, television show, book, or play titles which have been obscured through the use of synonyms. I make every effort to ensure that the titles I have selected are at least reasonably famous.

Feel free to look at earlier Oblique Title puzzles to get a better idea (for example, the first Oblique Title puzzle, or even the whole collection).

As usual, please refrain from leaving the answers in the comments, and instead send your answers to: mozglubov@gmail.com

1.) The Office of Modification

2.) 510nm Illumination Device

3.) Crimson Literary Symbol

4.) Consumes, Stalks & Exits

5.) Verified Falsehoods

6.) The Small Royal Son

7.) Occupant Wickedness

8.) CRUSH

9.) Searching for Kind Thoughts

10.) Large Noise Conjecture

11.) Contest of Feudal Seats of Power

12.) The Windstorm

Puzzle Number 14: Fair Game?

We have just started looking in detail at randomized algorithms in my computational complexity course. In addition to being a fascinating topic, it is also full of all sorts of fantastic results that make for great puzzles.

This puzzle takes the form of a game for two players, Player A and Player B. Player A has two cards, and he must write a distinct non-negative integer on each card, then lie that card face down on the table. Player B then chooses to flip over the card either on the right or the left, view the value of the number recorded, and must guess whether that value is greater than or less than the number on the other card. Player A is sneaky, however, and adds a rule that Player B must tell Player A the method he will use for determining his guess before they play the game (and Player B is not allowed to deviate from it).

Even with Player A trying to obtain an unfair advantage, it is relatively straightforward to show that Player B can still come up with an algorithm to make his guess that will make the game a fair one (each player has an identical chance of winning):

Player B's Fair Strategy:

Flip over the left card.
If that card has the value 0, guess that the other card's value is larger;
Else randomly (with a 50% chance either way) guess that the other card's value is larger or smaller.

Knowing this strategy ahead of time, Player A will obviously never put a zero on the left-hand card. Other than that, however, there is nothing he can do to increase his odds of winning above 50%, and the game is therefore fair.

Is this the best that Player B can do, or is there an alternative algorithm that he can use that will put his chances of winning above 50%? If there is, what is that algorithm?

Puzzles!

Today Sarah has a whole collection of puzzles posted in honour of Martin Gardner. You should definitely go have a look.

Puzzle Number 13: The Phantom Titles

Although it was only two puzzles ago that I last did an oblique title set, the fact that I took a long break from puzzle posting means it has still been a while (plus, these puzzles are the most fun to make). As usual, the puzzle consists of a set of titles pulled from movies, television shows, and literary works (and, occasionally, more than one of those categories) and then obfuscated with synonyms and alternative definitions; your task is to determine the original title.

1.) Epic Stories of the Collapse

2.) Exponential Parkland Protectors

3.) Firearms, Pathogens, and Carbon-Iron Alloys

4.) Meeting with the Seventh Avatar of Vishnu

5.) Fortified Domicile

6.) Happiness

7.) Excellent Future Notions

8.) The Hilarity of Mistakes

9.) No Sound from the Cowboy Film Forward Face

10.) Ferric Guy

As usual, send your solutions to mozglubov@gmail.com

Note: Solutions can be found here.

Puzzle Number 12: Code Breakers

In honour of recent contributions in encryption made by researchers at the University of Toronto, I thought I would finally come out with a new puzzle. In this puzzle, I have designed a relatively simple encryption algorithm (one that could easily be implemented either by hand or on a computer) and used it to encode two messages. The messages are both under the category of 'Classic science fiction film and television', but are otherwise unrelated. In order to make the puzzle somewhat more reasonable, I will point that all non-alphanumeric characters (punctuation) have been unchanged and are not involved in the encryption. Also, I only used a single case for the letters (in this case, capital) simply to make my life easier.

Message 1:
GDL4J9H3: HE5H2 G7D2BL5A6 G8FCBHD9H5F. HE1H1GH2 L8FH2 HE8H2 JCML9F3H1G CG2 HE6H4 GHL3FGE8D5D H5BHH9FDFD2GH7. D7HG G3D5JH0-MH0L5F AD7GGD9CB: HC H1LDA5CFH4 GHFL0BF3H1 BH7K KCFA3I5G, HC GH1H6B2 CIH BH6K A6D7G4H0 L2BI9 BH1K J8D5JD9A0D4NL1HD9CBG, HC K0CA7I8A8M F0C KE3H2FH8 BC AL4B E9L1G F2CBH1 K1H8G5CFH5.

Message 2:
L1 A8CBF6 HD3AH5 L4F0C D2B L1 F1L2A4L0LM G9L9F, G4L4F L3KL9M... GHL3F KL1FG

Good luck, and remember to send in your answers (or clarifying questions) to mozglubov@gmail.com.

Note: Puzzle solutions found here.

Puzzle Number 11: The Oblique Titles Strike Back

Clearly I didn't plan out my oblique title puzzle names properly, since The Return of the Oblique Titles preceded The Oblique Titles Strike Back. Oh well, hopefully my lapse in foresight will be overlooked by the great fun to be had in decoding the next set of titles. As before, these are a set of titles pulled from movies, television shows, and literary works (and, occasionally, more than one of those categories) and then obfuscated with synonyms and alternative definitions. I think a couple of these are rather challenging, so have fun!

1.) At an Unknown Location

2.) The Manner in which I Became Acquainted with Your Most Recent Female Progenitor

3.) The Misplaced Planet

4.) Lampyridae

5.) Vigorously Cleans

6.) A Story About Two Population Centres

7.) According to Your Preference

8.) Personal Graphical Representation

9.) No Rural Region for Elderly Males

10.) Overcook Announcement

Note: Anyone who gets #4 without looking it up has earned some profound trivial respect.

Note: Solutions can be found here.

Puzzle Number 10: Tetris Shape Reconstruction

Although not exactly mathematically oriented per se, this puzzle involves spatial reasoning and is certainly not verbally oriented, so I thought it could count. The idea is, given the screen shot of a hypothetical Tetris variant with fourteen horizontal cells shown below and the guarantee that no lines have been formed, can you determine a unique colour assignment to the traditional Tetris shapes (which can be found in the Wikipedia article if one is not familiar with them)?

Being unique, there should not be an additional colour assignment that also functions for the given image.

(Note: The last line previously held a typo which gave it a confusing double-negative... sorry about that)

Note: Solution to the puzzle can be found here.

Puzzle Number 9: Final Hint

This post is a couple days late, mostly because it is the Thanksgiving long weekend in Canada which threw my "update on the weekend" clock off. Anyway, now I am finally get around to it. As promised, the last hint for Puzzle Number 9 will outline the number of letters and punctuation in each of the planned sentences. As before, I am also open to novel solutions. The clue is given using the following notation: in parentheses, the word length is given. If the word is a contraction, the number of letters before the apostrophe is given, then the apostrophe, followed by the number of letters after the apostrophe. The punctuation at the end is the punctuation at the end of the sentence.

1.) A A C G G H H H I I I L M N N N O O R S T T U W Y
Six words, one is a contraction.
(3'1) (4) (8) (2) (2) (5)?

2.) A A A E E E E E E E E E F G H H H H I I N O O P P R R R R S S S S S T T T T T V Y
Eight words, none are contractions.
(5) (3) (3) (7) (2) (3) (8) (10).

Puzzle Number 9: Hint One

As promised, here is the first set of hints for puzzle number 9. I should also point out that one person has sent in solutions that use all of the letters (and are totally unrelated to my starting sentences, so clearly there are other possibilities). Of course, one of the solutions is not actually intelligible, but it is still a set of real words that use all of the letters.

Anyway, this hint gives the number of words in each "official" sentence (in other words, the one I started with to come up with the letter list). On the weekend I will release the number of letters in each word along with the punctuation in the sentence, before giving the answers next week. Of course, one should not feel constrained by the hints. Novel solutions are still very much appreciated. Please just point out whether or not you used the hints in coming up with your solution.

1.) A A C G G H H H I I I L M N N N O O R S T T U W Y
Six words, one is a contraction.

2.) A A A E E E E E E E E E F G H H H H I I N O O P P R R R R S S S S S T T T T T V Y
Eight words, none are contractions.

Puzzle Number 9: Epic Word Scramble

In a QI episode from the second season (or, I should say second series, since I am talking about a British show), Jimmy Carr did one of the most impressive things I have seen on television. Given a jumble of the following letters: A A A A A B B C E E E E E E G H I I K K K L L L M M M N O O O P R R S S S S S T T T T T T U U W, he was able to use them all to create the message "PUT SMARTIES TUBES ON CATS LEGS, MAKE THEM WALK LIKE A ROBOT" (of course, he did not have a comma, but I think that is something that he can be forgiven for). In recognition of such an impressive feat, I have created two sets of letters to be unscrambled. In this case, I have started with an intelligible sentence, so you can be assured that it is possible to use all the letters. If you are unable to, however, I will also accept solutions that simply use as many letters as you can manage for partial credit, with bonus given to amusing and interesting creations. If you are not particularly skilled at anagrams (like me), I will be posting two sets of hints in the next week. The first hint set will give the number of words that my original sentence contains, and the second will give the number of letters in each word as well as the punctuation between them. The first hint set should come out on Wednesday, so if you want to be really impressive and solve this without hints, you will have to get your solutions in before then. Note: Since you can add punctuation, contractions are acceptable (for example, CANT could be used not only as the word cant, but also to denote can't).

1.) A A C G G H H H I I I L M N N N O O R S T T U W Y

2.) A A A E E E E E E E E E F G H H H H I I N O O P P R R R R S S S S S T T T T T V Y

Hints: Puzzle Number 9 Hint One, Puzzle Number 9 Hint Two

Note: Solutions to the puzzle can be found here.

I'm a Role Model...

I seem to have rubbed off on my friend Scott, as he has begun publishing puzzles as well, starting with this one. I'm still thinking it over in the back of my head while I ostensibly get some work done...

Puzzle Number 8: Return of the Oblique Titles

As they seem to be more popular than my other puzzle forms (and they are easy and fun to think up during brief breaks from work throughout the day), I thought I would put up another set of oblique titles for people to ponder while I get my work and studying done. Here are ten more titles of books, movies, and television shows (with a couple that fall into more than one category) that have been obscured by rewording. Have fun!

1.) Every Canine Travels to Space

2.) Strange Peeper

3.) The Soricidae Domestication

4.) Stopping Device, Inventory, And a Pair of Wooden Containers Giving off Vapour

5.) Ritual Starvation and Feeling Enraged

6.) The Sightless Horologist

7.) Story Breakers

8.) Conflict Cudgel

9.) Maritime Marauders of the West Indies: The Profanity of the Dark Mollusk Bead

10.) The Quiet Equine Speaker

Note: Solutions can be found here.

Puzzle Number 7 Errata

As Scott brought to my attention, part of Puzzle 7 was poorly worded. I have corrected it in the actual post, but wanted to post something quickly pointing that out as well.

Each element of an alphabet must be constructed so that all molecules are bound to at least one other molecule in its network, but not all bonds need to be activated on a given molecule, thus allowing distinct and distinguishable bond networks to be constructed.

This is not worded the most clearly... what I was trying to say was that all elements of the alphabet must be connected (in other words, you cannot have two pairs of bound A molecules that are disconnected), but not all bonds within the network need to be activated. Also, your company can distinguish the difference between different bond arrangements and not just the total number of bonds.

Puzzle Number 7: Molecular Tagging

Taking a break from the word puzzles, I thought I would offer a more science oriented puzzle. I am not sure if my puzzle scenario is entirely clear, however, so if you have any questions please don't hesitate to send an email or leave a comment.

The Puzzle: You are working for a nanotechnology company on a project that involves suspending small molecules in a solution and subsequent detection as a method of labeling (kind of like a chemical bar-code). Your company has developed two possible compounds to use, and wants you to determine whether one compound is better (although it is possible there is no difference). Compound A is a relatively simple molecule and can be activated to form non-polar bonds with up to three other A molecules. Compound B is slightly more complicated, and has two different types of binding sites that can be activated to form polar bonds with the complementary binding sites on up to two other B molecules. Bonds need to be activated to form, so molecules will not spontaneously bond in solution. Your company can detect the presence and polarity of a bond when analysing the compound in a solution.

Two A molecules bound together.

Two B molecules bound with unequal polar bonds.

Due to the higher complexity of molecule B, it costs the same amount of money to synthesize three B molecules as four A molecules. Your project leader therefore wants you to decide between two different molecular alphabets: either four A molecules with varying intermolecular bonds or three B molecules with varying intermolecular bonds. Each element of an alphabet must be constructed so that all molecules are bound to a single network, but not all bonds need to be activated on a given molecule, thus allowing distinct and distinguishable bond networks to be constructed.

Your task, therefore, is to determine whether networks of four A molecules or three B molecules are more effective at encoding information.

Note: Yes, I made the diagrams in Paint. Yes, they are ugly. Hopefully, though, they get the point across clearly.

Note: Solutions to the puzzle can be found here.

Puzzle Number 6: Star Media Quotations

This is a light-hearted weekend puzzle based on a game my research partner and I played last summer while performing the tedious task of mixing electrode paste for our EEG cap. The game my friend and I played was to take turns saying a line from one of the original Star Wars movies (I limited it to those because I had only seen the new ones once each), and then the other person had to try and name who said it, to whom, and what the context was. For this puzzle, I have extended it to include television shows with star in the name. This should increase the difficulty somewhat, although I have tried to pick at least somewhat memorable lines. So, to be clear, the task for each quotation is to name the movie or television show it is from, who is saying it, to whom it is being said, and the general context of the scene. Occasionally, there is more than one context or listener, but those should hopefully be fairly obvious. Also, I came up with most of these by memory, so if I've made any errors, please be sure to let me know. Also, as usual, partial solutions are also welcome.

1.) "I'll make it up to him next year; I promise."

2.) "There are four lights!"

3.) "He is as clumsy as he is stupid. General, prepare your troops for a ground assault."

4.) "Welcome home, Mr. President."

5.) "Yub yub."

6.) "your basic hedonistic predilection for rhythmic stroking of your fur, to demonstrate affection."

7.) "I've lost the fellatus to speak properly."

8.) "sometimes a cake is just a cake."

9.) "Hey, look! I'm an engineer! I can do math!"

10.) "I can arrange that. You could use a good kiss!"

Note: Solutions can be found here.

Puzzle 5 Extension

I was planning on posting the solutions to Puzzle Number 5 today, but there are a couple as-yet unsolved titles. Therefore, I thought I would give people a reminder to check the puzzle out and then a couple more days to think about it and try to solve them all (even if you have not solved them all, feel free to send me the ones you think you know. I do give credit for partial solutions, too!).

Puzzle Number 5: More Oblique Titles

I apologize for the lack of science and mathematics in the last little while (since that is, ostensibly, what this blog is about), but I have been fairly busy with being moderately sick and, when not sick, trying to conduct research at the Institute. To hopefully tie my readers over with a little more intellectual stimulation, here is another set of oblique titles. In order to make this a little more challenging (and perhaps to entice those in my audience who do not associate with the vulgar media of television and film), I have introduced book titles into the mix of film and television show titles. While most book titles are either from relatively recent best-sellers or classics that I would expect the majority of people to at least recognize, I do admit that there is one random smut novel title thrown into the mix just because I find it funny (for the record, I never actually read the book... just hid it in my best friend's backpack in grade 8 as a joke).

Here are the new titles to be deciphered:

1.) The Second Finisher: Day of Giving One's Opinion

2.) The Correct Cost

3.) Thinking Something Grand is on the Way

4.) Deities from the New World

5.) Leading up to a Base

6.) Two Dozen

7.) A Period of Time in Which a Certain Female Acted Naughty

8.) Law Breaking and Retribution

9.) The Vitis Fruits of Anger

10.) Rhythmic Body Gyrations with Lupine Companions

11.) The Inexplicable Nocturnal Canine Event

12.) The Ruler of the Outer Tent Linings

Good luck to all.

Note: Solutions are available here.

Puzzle Number 4: Oblique Title Puzzle

Taking a cue from the enjoyable puzzle I linked to a week and a half ago, I have created a similar puzzle (but with words instead of images). So, the idea is I have come up with a smattering of movies and television shows, and rewritten their titles with synonyms and definitions. So, for example, Cease Living with Great Impact would be Die Hard.

As usual, feel free to send your solutions to me (so as not to spoil the puzzle for others by leaving them in the comments) at mozglubov@gmail.com. When I publish the solutions in a few days I will be sure to mention who solved which titles.

So, here are the rewritten titles:

1.) Best Firearm

2.) Martial Engagements of a Stellar Nature: A Recent Sentiment for a Positive Outcome

3.) Foreigner Against Hunter

4.) Growth Prevented By Legal Restraint

5.) Veritable Sanguine Fluid

6.) The Ruler of the Circles: The Monarch Comes Back

7.) Visual Receptors of a Serpent

8.) Famous Person Hike: Traveler

Note: The solutions can be found here.