Welcome to
Joseph Young’s Puzzle –ria!
It is Friday, December 12. Let us begin this week's festivities with a timely mathematics puzzle.
Some of the numbers will be familiar to number theorists and other number nuts (Please note, that is “number” with an “-er” at the end!)
Bonus Timely Slice:
Groundhog Day-after
Name the final number in this sequence:
Groundhog Day-after
Name the final number in this sequence:
6, 24, 60, 120, 210, 336, 504, 720, 990,
1320, 1716, ____
(There is no significance in my
omission of commas from the four-digit integers. With the commas between the
integers, it just seemed too confusing to place commas also within some integers.)
Besides naming the final number,
explain the significance of the sequence. Your explanation will likely
account for why is there no Nth number in the sequence for N > 12, at least not
in the world we live in. Mathematically, however, the sequence of course
extends infinitely (as do most things mathy, either infinitely or infinitesimally).
Express the value of the Nth integer in
the sequence as a ratio in terms of N.
Hints:
One number pertains to the day after
Groundhog Day (the day that Phil Connors {portrayed by Bill Murray} was seemingly
in danger of never waking up to) in a year that was one in a seven-consecutive-year
streak in which Punxsutawney Phil saw his shadow.
One number pertains to the eve of the
tenth anniversary of 9/11.
One number pertains to the day “Three Studies of Lucian Freud,” a series of portraits of Lucian Freud by the British painter Francis Bacon, sold for $142.4 million in a New York City auction, setting a new world
record for an auctioned work of art (see illustrations above… for free!).
One number (not shown) pertains to tomorrow.
Two weeks ago Dr. Will Shortz, National Public Radio Weekend Edition Sunday puzzle
master, laid some “amazing wordplay” on us. ...
But now for something completely amazing in a different kind of way. (Thanks to Rose, my friend, former co-worker and design whiz, for tipping me off to the buzz about this “labyrinthinazi” wrapping paper pattern.)
Okay, that’s a wrap. Now here is this week’s
trio of fresh Puzzleria! slices:
Menu
Sporty Easy As Pie Slice:
Hippo Triple-Team
Name an event – in two
words, one of them an initialism – that takes place on a field. Three teams
share the field, all uniformed and all with equine nicknames. Each team’s
uniform reflects its nickname.
At any one time, the number of team members
on the field for any one team rhymes with the other two team-member numbers.
Two of the teams, whose nicknames are official, consist of backs, linebackers
and linemen.
The third team, with fewer members and a nickname that is unofficial, jocular
(and perhaps mildly derisive), consists of a head linesman and others.
Reverse the fourth and fifth letters
of the event and move its first letter to the end, resulting in a second
possible, but less jocular and derisive, nickname for members of the third
team. (Hint: No, it’s not “scrubs!”)
What are the event and the second nickname of the “third team”?
Extra credit: What are the nicknames of the two larger teams and the other, more jocular, nickname of the third team?
Superfluous hint: A member of one team participated in league championship games for both of the larger teams.
(Un)conventional Slice:Police and Politicos
Think of a word associated with
“conventional” politicians who are not the silent type.
Rearrange all but the
first three letters to form a word associated with unconventional policemen who
are the silent type.
What are these two words?
Big Band Slice:
Jazz Guzzlers
Take an adjective associated with a
particular jazz band popular in the mid-20th century.
Remove the
fourth letter and divide the result into two words that each can mean “to drink or
take in sustenance.”
What are these three words? What is the popular jazz band?
Every Friday at
Joseph Young’s Puzzle -ria! we publish a new menu of fresh word puzzles, number
puzzles, logic puzzles, puzzles of all varieties and flavors. We cater to
cravers of scrumptious puzzles!
Our master chef, Grecian gourmet puzzle-creator Lego Lambda, blends and bakes up mysterious (and sometimes questionable) toppings and spices (such as alphabet soup, Mobius bacon strips, diced snake eyes, cubed radishes, “hominym” grits, anagraham crackers, rhyme thyme and sage sprinklings.)
Please post
your comments below. Feel free also to post clever and subtle hints that do not
give the puzzle answers away. Please wait until after 3 p.m. Eastern Time on
Tuesdays to post your answers and explain your hints about the puzzles. We
serve up at least one fresh puzzle every Friday.
We invite you to make it a habit to “Meet at Joe’s!” If you enjoy our weekly puzzle party, please tell your friends about Joseph Young’s Puzzle -ria! Thank you.
Saturday's date is already getting a lot of hype here so the number puzzle came easily.
ReplyDeleteMy two cents: the new type in the comments section is harder to read than say, Arial. . .
Enya_and_Weird_Al_fan,
ReplyDeleteI agree with Word Woman that the Courier font is a bit tougher to read than, say, Arial (Thanks, WW, for the suggestion.)
The solution, I believe, it to return to Arial for our comments. But if you have word squares or other graphics to share, we could always use Courier on an ad hoc basis. Can you please give me your input?
I will explore if there is a way for Blogger to retain Courier for the week you posted your fine graphics, but I doubt if there is. I may also explore if there is a font at my disposal that is easily readable but also works well with graphics.
Uh, so, anything you could do to, uh, to help would be ... very ... helpful.
LegoEccentricFontPerformance
legolambda,
DeleteAny chance your fine puzzle blog here could have two comment sections?
A courier comment section could perhaps be set up following the regular comment section, and posters who use it could also make a post in the regular comment section including a "Please see my comment in the Courier section below" note.
P.S.: I was thinking of reposting the puzzle filling in all 16 cells having numbers in the same position as in Ben Franklin's.
Woah!!
DeleteYou had to return the font for the week beginning Friday, November 28, 2014 to the Ariel font ALSO!?!?
Sheeesh!!!! Just how strict IS Blogger's policy??
Sorry, I meant "Whoa!!"
DeleteJust to be obnoxious:
ReplyDelete0.0619047619047
Beetle's buddy has disdain for temporary sleeping arrangements; tells everybody.
10-4
0.047368421052631578947368... and that's my final offer.
DeleteA paraphrase of an anagram of the three team nicknames (yes, that Beetle).
The empty space indicates I have no answer for this one.
Just something Broderick Crawford used to say.
Paul,
DeleteRegarding your decimals, see my reply to David, below.
Your anagram actually makes sense! Impressive. Beetle’s buddy suspects there are snipers hiding in nearby farmer’s overgrown field. So he lobs a grenade where he thinks they’re lurking.
Senseless, compared to yours.
I grew up in the 1950s on Highway Patrol, Sea Hunt (Lloyd Bridges), M Squad (Lee Marvin) and scores of westerns. It was in pre-cable days, with only one TV station within range, an NBC affiliate.
Broderick Crawford was the epitome of “gruff.” His 10-4 in this episode appears at about the 4:10 mark.
LegoRabbitEarsHorizontalHold
Nice solving in a short time frame.
DeleteI doubt that BC ever said "10-4, good buddy". And, as you're obviously aware LM had swinginger theme music.
Zero lobs at corn --B.S. ??
DeleteAnyway,
I think David's decimal refers to 12/13/14, and my first one pertained to 13/14/15, just because I'm obnoxious. My second decimal hints at the Bahá'í calendar, also called the Badí' calendar.
Paul,
DeleteI swear the M Squad/Count Basie connection was sheer coincidence! Thanks for linking the M Squad theme. While on YouTube. I couldn’t resist playing the Henry Mancini Peter Gunn theme. Most upbeat and downswingingest! (thanks, ron.) Lotta great theme music in that era.
BRONCOS + COLTS + ZEBRAS = ZERO BLASTS CORNCOBS
Regarding the Cotsworth calendar:
One-score-and-eight days hath September,
April, June, as well, November.
All the rest hath twenty-eight…
Except we add one monthless date
At year’s end and, by protocol
In leap years, between June and Sol.
Call me “loony,” but I actually like this moon-based notion for marking time. (But we’ve gotta come up with something better than “Year Day” for the last day of the year!).
The Baha i/Badi calendar has appeal too. You can’t beat 19 months of 19 days each, and four or five days of Ha between Mulk and Ala.
Oh, and it is the eve of the 25th day of Kislev on the Jewish calendar. Happy Hanukkah!
LegoZeroQuestionsCotsWorth
So, I have had a busy last couple days, including a trip to Pittsburgh. I have the BTS and the SEAPS, but not the (U)S and BBS.
ReplyDeleteI can be obnoxious, sort of like Paul, but fewer decimal places: 0.065934066
(U)S hint: To illustrate the puzzle I tried finding a summer of '68 photo of police and politicos in Chigago, but was unsuccessful.
DeleteBBS hint: Ah one, and ah two, and ah three...
I do not think either David or Paul is obnoxious. But their decimals point me in no direction.
LegoBaffled
Ok, about the fonts....
ReplyDeleteI notice that you've returned the font of our comments back to Courier. Thank you. However...
Apparently you've either slightly increased the width of each individual font, or else you've slightly decreased the width of each line of our posts. The result is that in the week beginning Friday, November 28, 2014 (its last week available here without selecting "Older Post"), a lot of my graphics are readable again, but the main one, the side-by-side comparison of two 8x8 squares, that's now messed up; because those lines which were short enough originally (although just barely) that week are now just a little too long now!
Enya_and_Weird_Al_fan,
DeleteSorry. While tinkering with Blogger I probably switched the font size somehow. I'll work on restoring it.
Incidentally Blogger does provide a long list of fonts one can use for comments. Are you aware of any font besides Courier that works with your graphics? I plan to experiment to see if any do work. I'll try not to goof anything else up though!
LegoTinkeringToying
I decided to try out different fonts in EditPad Lite. To my surprise, what I thought was its default (Courier New) IS NOT!!
DeleteIt's "Consolas 10"! Consolas has the g's you probably don't like. (Uncooperative in your 'Hale Boggs' puzzle the week beginning Friday, November 14.), but it does look pretty good. I'm betting the makers of EditPad looked over fonts pretty well when they chose it for their default.
Enya_and_Weird_Al_fan,
DeleteI just visited Blogger. There is no Consolas 10 at my disposal, but there is just plain Consolas. So I tried the Consolas font in 12px, 11px, 13px and 14px font sizes, but none of them worked with your large grids from Nov. 28. So I returned to Courier 12px.
I am always open to your suggestions and greater expertise in these matters. Thanks.
LegoDisconsolas
BTS:
ReplyDeleteThe series actually starts at 0,0,6,24,60,120,210... The formula for the next number is Nx(N-1)x(N-2).
No ratio necessary. So for the 14th number in this series that starts at the first 0 (the one after 1716) is 14x13x12 = 2184. The next number, the 15th in this series, would be 15x14x13 = 2730. The first zero where N = 1 is therefore 1x0x-1 = 0. The second zero where N = 2 is therefore 2x1x0 = 0. The third number where N = 3 is therefore 3x2x1 = 6. The fourth number where N = 4 is therefore 4x3x2 = 24 and so on.
UnCS:
“PRECOGNITION” is something “talkative politicians” claim to have. Drop PRE and rearrange the remaining letters to yield: “INCOGNITO” a word associated with silent policemen!
BBS:
A “SWINGDOWN” band. This yields “SWIG” + “DOWN” - The best I can do! If you remove the fifth letter from the word, then DOWNBEAT works. (DOWN+EAT)
Ron-
DeleteLego's series were potential month/day/(2 digit)years, so started with 1/2/03 (1*2*3=6), ending with last Saturday's 12/13/14 (12*13*14=2184). My decimal is 12/13/14 (since that the way it is written) = 0.065934066 (which is how many places my calculator displays).
For SEAPS, I had Broncos, Colts, Zebras (referees) / NFL Game / Flagmen.
For BBS, I didn't get past swing / swig.
"Mathematically the sequence extends infinitely..." I have just given the mathematical formula for that sequence. Also I thought "Rearrange all but the first three letters" to mean "drop the first three letters and rearrange the remaining letters."
Deleteron,
DeleteYou are 100-percent correct about the (U)CS. My wording was ambiguous at best. (This is why I try to count to ten before criticizing Will’s Shortz’s NPR puzzles. I don’t want to be seen as the pot calling the grass green.)
Your “precognition/incognito” answer is excellent also. It is four letters longer than my “-notes/-stone” effort. And it is still a letter longer even if you apply the “key” to their fronts (as one might apply a key to a liquor cabinet containing SHErry and wHISkey!).
What’s more, “precognition” rhymes with “politician.”
And your coinage of “swingdown” is inspired too. Reminds me of “smackdown dragout fight.”… “The band played upbeat swingdown blues!”
Also, DOWNBEAT – B = DOWN + EAT is a nifty piggyback puzzle.
Great contributions, as usual, to you and all who post here.
Thank you also for your elegant formula in terms of N: the Nth number in the sequence that begins 0, 0, 6, 24, 60, 120, 210... = (N) (N - 1) (N - 2). The ratio I was thinking of involved factorials! That's more cumbersome unless you have a factorial chart at hand or a factorial function on your calculator.
My ratio in terms of N is (N + 2)! / (N – 1)!, which works for N = 1 only because 0! is defined as 1.
So, the Nth number in the sequence that begins 6, 24, 60, 120, 210, 336, 504 etc… is has a value of (N + 2)! / (N – 1)!
I hope to say more about these formulas (for those who think more visually) in a later post.
LegoCognito
For the record, here are the answers to the trio of Puzzleria! house slices:
ReplyDeleteSporty Easy As Pie Slice:
Hippo Triple Team
Name an event – in two words, one of them an initialism – that takes place on a field. Three teams share the field, all uniformed and all with equine nicknames. Each team’s uniform reflects its nickname.
At any one time, the number of team members on the field for any one team rhymes with the other two team-member numbers. Two of the teams, whose nicknames are official, consist of backs, linebackers and linemen. The third team, with fewer members and a nickname that is jocular (and perhaps mildly derisive), consists of a head linesman and others.
Reverse the fourth and fifth letters of the event and move its first letter to the end, resulting in a second possible, but less jocular and derisive, nickname for members of the third team. (Hint: No, it’s not “scrubs!”)
What are the event and this second “third team” nickname?
Superfluous hint: A member of one team participated in championship games for both of the larger teams.
Answer:
NFL GAME; FLAGMEN
Team nicknames: Indianapolis COLTS; Denver BRONCOS (eleven players per team on the field) ; ZEBRAS (the seven-member officiating team, which wears shirts with black and white vertical stripes)
“Super”fluous hint: Denver Bronco QB Peyton Manning appeared in Super Bowls both as a Colt and Bronco.
(Un)conventional Slice:
Police and Politicos
Think of a word associated with “conventional” politicians who are not the silent type. Rearrange all but the first three letters to form a word associated with unconventional policemen who are the silent type.
What are these two words?
Answer:
KEYNOTES (keynote addresses, delivered at political conventions)
KEYSTONE ( Kops)
Big Band Slice:
Jazz Guzzlers
Take an adjective associated with a particular jazz band popular in the mid-20th century. Remove the fourth letter and divide the result into two words that each can mean “to drink or take in sustenance.” What are these three words?
”Swingingest”
Swig
Ingest
Lego...
A fourth answer for the recoed, and some comments:
ReplyDeleteBonus Timely Slice:
Groundhog Day-after
Name the final number in this sequence:
6, 24, 60, 120, 210, 336, 504, 720, 990, 1320, 1716, ____
Besides naming the final number, explain the significance of the sequence. Your explanation will likely account for why is there no Nth number in the sequence for N > 12, at least not in the world we live in. Mathematically, however, the sequence of course extends infinitely (as do most things mathy, either infinitely or infinitesimally).
Express the value of the Nth integer in the sequence as a ratio in terms of N.
Answer:
2184
It is the product of the three numbers in the date 12/13/14, December 13, 2014.
With (month/date/year, last two digits) notation, 12/13/14, December 13, 2014, is the final date of this century that can be written with consecutive integers in the correct order. The first was Jan. 2, 2003 (01/02/03, with a product of 6); the second was Feb. 3, 2004, with a product of 24; the third was March 4, 2005, with a product of 60; etc.
The next such date, January 2, 2103, will begin another string of twelve dates roughly 13 months apart in the 22nd Century, beginning with January 2, 2103 (01/02/03).
My sequence ends after twelve integers because our calendar has only twelve months, so there is no 13/14/15 or 14/15/16 etc. That is, there is no Undecember 14, 2015 (“A very merry Undecember to you!) or Duodecember 15, 2016, etc.). Although Paul cleverly hinted at 13-month and 19-month calendar years with his decimal hints (that befuddled me!).
My hints:
One number (24) pertains to the day after Groundhog Day, February 3, 2004 (02/03/04), in a year (2004) that was one in a seven-consecutive-year streak (2000-2006) in which Punxsutawney Phil saw his shadow. (As you can see from this chart, Punxsutawney, PA seems to be sunnier than San Diego, CA!)
One number (990) pertains to (09/10/11) the eve of the tenth anniversary of 9/11.
One number (1716) pertains to November 12, 2013 (11/12/13), the day “Three Studies of Lucian Freud,” a series of portraits of Lucian Freud by the British painter Francis Bacon, sold for $142.4 million in a New York City auction.
One number (not shown, but 2184) pertains to tomorrow. I uploaded the blog on December 12, 2014. “Tomorrow” was 12/13/14, December 13, 2014.
LegoCotsUnworhy
I am ashamed to admit that I whiffed on Paul’s and, later, David’s decimal clues for my Bonus Timely Slice (BTS).
ReplyDeleteAfter all, (I think) I invented the notion of assigning a decimal (not necessarily a unique decimal) to each day of the year by dividing its month number by its date number in my July 4 Con-number-umm Slice, “ Deciphering Decimals.”
Paul and David took that notion a step further by then dividing that result by the day’s year number. For example 12/13/14 equals David’s decimal, 0.065934066, or 0.92307692 divided by 14.
Of course you have to perform the two divisions in order, from left to right (or from top to bottom). Dividing 13 by 14 (0.92857…) and then dividing 12 by that quotient yields not 0.065934066 but 12.923…
Interestingly, because in a string of divisions such as 12/13/14 or 12/13/14/15/16/17, the only numerator (dividend) is the number at the far left. All other numbers to its right are denominators (divisors) which can be multiplied together, with their product then divided into the dividend.
This works because dividing by a number by N is like multiplying it by N’s reciprocal.
For example, David’s decimal 0.065934066 = 12/(13x14) = 12/182, or, multiplying with reciprocals, 12/1 x 1/13 x 1/14.
And, in the longer example, 12/13/14/15/16/17 = 12/(13x14x15x16x17) = 12/742,560. When working with larger numbers, this method results in less round-off error.
Paul’s decimals were not “obnoxious,” as he claimed, but they were deviously clever. His first example, the repeating decimal 0.0619047619047…, is the date 13/14/15, December, 14, 2015 in the lunar-based Cotsworth Calendar, in which every month has 28 days and December is the thirteenth month.
Paul’s second example was another repeating decimal, 0.0473684210526315789, which is 18/19/20, the nineteenth day in the month of Mulk, the eighteenth month in the Baha’I, or Badi’ calendar year of 2020.
BTW, Paul, how do you reckon them Duke boys, Bo and Luke, would fare against the likes of Bro and Lee, compared to them Hazzard County constables they is eternally eluding?
LegoGeneralLeembda
Sorry, Lego; no opinion. Never was much of a Hazzard fan.
DeletePaul,
DeleteThanks for the great link of Ellington Mae Duke… Or is that Ellie Mae Clampett in “The Dukes of Beverly Hills”? I’m afraid I might have my hillbillies mixed up! And my Ellies and Ellingtons, and Daisies, Mazies and Maes.
LegoHillBillyStrayhornHillBillieHolidayGreetings