stolf’s blog 593: rectangles ?!?!?

0

You did the SQUARES…now how many RECTANGLES?

…bearing in mind that a square counts as a rectangle. At first this seemed like a daunting task, but once I got around to organizing a plan of attack, it wasn’t hard at all. Took me under 5 minutes. Really? Sure…let’s take it step by step…

And that plan of attack was to classify rectangles by their size, based on the unit square, seen below in red. Rectangles would be AxB…that is, A is the length down and B is the length across. Below for example we have 1×2 in purple and 3×4 in green…

r1

Next, we list all the possibilities, remembering that we’ve already done AxA…those were the squares…

plan of attack

That’s 12 types of rectangles in all…but there’s a short-cut…we only have to count 6 types, then double that total. You can see why demonstrated below with 1×4…flip the puzzle on its side by rotating it 90 degrees, and you have the same number for 4×1 as you had for 1×4.

r2

That’s pretty much all there is to it…take the rectangles type by type…count carefully and keep a running total.

1x2 1x3 1x4 2x3 2x4 3x4

Now add in the mini-rectangles…plus the 40 squares from the last puzzle…and we’re done…grand total = 118.

mini

______________________________________________________

Copyright © 2012 Mark John, All Rights Reserved

shameless plugs…be there or be round…

Other  Blog at https://stolf.wordpress.com  (the legendary Stolf’s Blog)

Podcasts at http://stolfpod.podBean.com  and   http://thewholething.podBean.com

More bloggage at  http://travelingcyst.blogspot.com

Updated Resume at   http://travelingcyst.blogspot.com/2011/02/resume.html

Audio samples at  http://stolfspots.podBean.com

Advertisements
Posted in Uncategorized | Leave a comment

stolf’s blog 592: How Many Squares?

0

The answer is: 40 squares…and seeing is believing!

Chart A…Where to begin? Well, apart from the mini-squares in the center, the smallest building block in the puzzle is what we might call a “unit square.” One of them is outlined in Chart A.

1

Chart B…And since the entire puzzle is a block of 4 unit squares horizontally and 4 unit squares vertically, that’s a total of 4 x 4 = 16 unit squares. We can call these 1×1 squares…that is, 1 square on each side. I know, since there’s only one unit square in a 1×1 configuration, how can you refer to “sides” plural, as implied by the phrase “each side”? It’s because of the curious but very useful mathematical fact that 1 x 1 = 1, that’s why.

Chart C…We then count the 2 unit squares in the center…

2

Chart D…And each of those is divided into 4 mini-squares…running total is now 26.


Chart E…
We next move on to the 2×2 squares, made up of 2 unit squares to a side. Chart E shows there are 9 of them. What a lot of people do is consider just the corner 2×2’s…the ones labeled 27, 29, 33, and 35. But as you can see, there are 2 more “centered” horizontally, 28 and 34…2 more “centered” vertically, 30 and 32…and a final 2×2 completely centered, 31. Running total is now 35.

3

Chart F…With the 3×3 squares, there really are only “corner” ones, the 4 shown in Chart F. That’s because the total puzzle is made up of 4×4 unit squares, and 4 is an even number…and with the 3×3 squares, 3 is an odd number. If the total puzzle had been 5×5, then there would be room for additional “centered” 3×3’s, you see? But here there is not. Move the corner square 36 over one unit square to “center” it, and you now have another corner, 37. So the running total is up to 39.

4

Chart G… And finally, don’t forget the total puzzle itself, a 4×4 square…grand total = 40. Done and done!

5

PS: With 40 the definitive answer, some of you may be disappointed that there’s nothing left to argue about…but have I got good news for you! I read one comment that said the answer depended on the “rules”…and I thought: What rules? A square’s a square…4 equal straight sides, 4 interior right angles…pretty straightforward to me. Well, and you have to follow the lines given in the puzzle…nothing like this, for example:

rules

But you know what? You should never underestimate the scope of people’s imaginations, however misguided. An earnest noodnik… whose website I will not dignify with a link, sorry…suggests there are 7 more “squares,” as follows…

duh

The arguments pro and con are obvious, so I won’t go into them…except to say I’m sticking with 40. OK, I will say this: It reminds me of when I worked at a radio station and we broadcast a scavenger hunt…one of the items was a unicycle. A lady brought in a Christmas tree ornament of Santa riding a unicycle…she didn’t get credit. This was maybe 25 years ago and I’ll bet she’s still sore.

______________________________________________________

Copyright © 2012 Mark John, All Rights Reserved

shameless plugs…be there or be…you know…

Other  Blog at https://stolf.wordpress.com  (the legendary Stolf’s Blog)

Podcasts at http://stolfpod.podBean.com  and   http://thewholething.podBean.com

More bloggage at  http://travelingcyst.blogspot.com

Updated Resume at   http://travelingcyst.blogspot.com/2011/02/resume.html

Audio samples at  http://stolfspots.podBean.com

Posted in Uncategorized | Leave a comment

For $5 I’ll Tell You Who’s Related How to Whom

Dear friends: Here’s the ad I put up on eBay classified today…

How are you and your grandmother’s cousin’s granddaughter related? If you have a PayPal account, I’ll tell you for $5. Yup, 5 bucks to finally know for sure…or confirm what you always thought. What’s $5…a bag of chips or a pack of smokes…almost a gallon of gas! Can you trust my answer? Do I know what I’m talking about? See for yourself…google G4BB (stands for Genealogy for Baby Boomers) and check out over 90 fun-filled posts. Here’s a sample of what you get…a color chart and a complete explanation emailed to you. And I’ll answer follow-up questions for free if there’s something you don’t understand. Send your question to stolfwx@hotmail.com, which is also my PayPal address.


Yup…this means YOU…$5 and I’ll sort it out for you…of course, you might find your answer somewhere here in my 90+ G4BB postings, but then sometimes even I can’t find something I’m looking for 😉 😉  So loosen those purse-strings and then at the next family reunion, you can prove them all wrong…ha ha!!

__________________________________________

Copyright © 2012 Mark John Astolfi, All Rights Reserved

Posted in Uncategorized | Leave a comment

stolf’s blog 9/10/2012

…read the recent on-line headline. Oh, really? Is that your final answer? “The team he moved to Baltimore” refers to the Cleveland Browns. Or does it? According to the NFL, the Cleveland Browns never went anywhere…Uncle Wiki sums it up nicely:

OK, that’s the NFL’s story, and they’re sticking to it…ditto the city of Cleveland, a bunch of cry-babies if ever there was one…and I say that with all due respect (which of course in this case turns out to be very little indeed) because my Dad came from Northeastern Ohio and I have tons of relatives there. Not in Cleveland proper, mind you…but that is their nearest “big city”…not that they have to like it, it’s just a geographical fact. So Art Modell dies, and talk about kicking a man when he’s down…and down for good. The Media was all abuzz with: Was he a bigger dirtbag than LeBron?

Nice. Actually, I guess all teams this weekend will be honoring the man, including the team he actually did move to Baltimore, the Baltimore Ravens. The interpretation of events which concludes that the Cleveland Browns stayed put…”de-activated” if you will…has never been employed before or since in the history of American professional team sports. You know, when dealing with antiques and other collectables, there is the concept of provenance…defined as “the chronology of the ownership or location of an object.” And that’s it in a nutshell.

The team Jim Brown played for moved to Baltimore, starting in 1996. No “legal settlement” can alter that fact. I mean, do the current Washington Nationals, the ex-Montreal Expos, claim Walter Johnson once pitched for their team? They’d have to argue with the Minnesota Twins for that honor…and if you’re going to think of it in that provincial way, then I reckon the Texas Rangers would have a dog in that fight, since they were also once upon a time the baseball team that played in our nation’s capital.

The whole thing is preposterous…especially to me, one of whose favorite pet peeves is Geographical Correctness…like, for example, there is no professional sports team in Tampa Bay…maybe water polo or synchronized swimming someday, but none at present. And the proof of the absurdity of it is a headline like the above…somebody thinks Modell moved the team from Cleveland to Baltimore, and certainly anyone reading that headline understands what they meant…except of course the official record says nothing of the sort ever happened.

In fact, when I first read that headline, I thought they were suggesting that the Baltimore Ravens had moved back to Cleveland…how else could a team in Cleveland salute the man who moved them…since the team that moved was not the Browns but the Ravens…except that’s not exactly right either…oh, phooey…who cares? Their way, the Cleveland Browns franchise has never made it to the Super Bowl…when of course the Ravens did it in that first season of 1996. And that’s enough for me…sez me.

 
 

B*A*K*E*R*S   D*O*Z*E*N

(1)  Maybe it’s not your style, and I understand that…but never
needing a “cover story” is such a tranquil way to live…IMHO…

(2)  Old saying: New crimes wake up old ones…

(3)  Vegetal is the trendy new way to use the word vegetable as
an adjective…altho “vegetal” can also mean “vegetative”…zzzzzzz…

(4)  …and I guess it’s just me, but anyone who says treble when they
mean triple or “times 3″…needs to join the real world and get a life…

(5)  After all these years, nice to see Jim Davis can still play around
with the physical conventions and visual cues of the comic strip …

(6)  That fly that just landed on my arm is thinking: You know,
it smells like crap…but when I alight, there’s no crap there…
and this happens over and over and over…what gives?…

(7)  …but along those same lines, if you think nobody wants
you, ask a mosquito…or for that matter, a tape-worm…

(8)  I don’t normally dig Doonebury’s political strips, but this one
just makes me laugh every time I read it…dead on, to be sure…

(9)  In the Fall, I like to sit on the front porch and eat
salted peanuts from the shell…and feed them to the
squirrels…and watch their ankles swell up…

(10)  And what fun this was, too…pull it out…put it back in…
pull it out…put it in…pull out…put in…out…in…wheeeee!…

(11)  I work for an old-school local radio station…if your pet
is lost, we’ll announce it on the air…heck, we’ll even lose it
for you…yes, we go that extra mile for our listeners…

(12)  To my baseball buddies: with 2 wild-card teams now, perhaps the
Magic Number for clinching the divisional top spot isn’t quite as urgent…
but for the record, it’s this: 163 – leader’s wins – trailer’s losses…

(13)  Next time you watch the 1962 movie Advise and Consent, you might want to look up Lester Callaway Hunt, Senator from Wyoming, who killed himself in his Senate office with a rifle from home on June 19, 1954…it’s complicated, as most of life is, but had to do with both failing health and  the threat that his homosexual son’s arrest would be made public…


POUTINE-ON-A-STICK

If you don’t get this, let your mouse hover over the picture, and the file-name I gave the image should appear and explain all…

POUTINE-ON-A-STICK EXTRA

Sure…except for this to actually make sense, wouldn’t the 2 fingers have to be sticking up where they would be visible in the photograph?…I’m just sayin’…

Posted in Uncategorized | Leave a comment

stolf’s blog for 9/3/2012…fast becoming the least-read on the net!

Once upon a time, I wanted to be a high school math teacher…in that alternate universe, I would have offered students extra credit for bringing in math mistakes from newspapers, advertisements, etc. So what do we make of this, from a review of a book about Strom Thurmond?

For the record, the South Carolina State Senate convenes on the second Tuesday of January…if that was the case in 1933, that would be January 10. His last day in the US Senate was January 3, 2003…he died in June of that year. Now technically, his political career, so-defined, lasted 6 days shy of 70 years. 3+6=10? Yes, because 70 years would have been “in the books” at the close of work on January 9, 2003…January 10th would have been the first day of his 71st year. Thus, if we round it up to 70 years even, he certainly had a career that lasted or ran for 7 decades.

The problem is the use of the word spanned. For example, the first professional baseball team, the Cincinnati Red Stockings, was established in 1869…thus it would be proper to say that baseball as a paid profession has spanned 3 centuries…altho it obviously hasn’t lasted or run for 300 years. When I read the above underlined quote, that’s certainly what I took it to mean, and immediately noticed the discrepancy.

Because the word decade can be used in 2 ways. Taken as any period of 10 years, Strom Thurmond’s 1st political decade was 1933-1942, his 7th was 1993-2002, plus 3 days into his 8th decade. The “span” here is 1st thru 8th. But a decade can also mean those 10 years identified by the same numeral in the tens place…thus the 20s, the 60s, the 90s, etc…and BTW, dunno how you do it, but I call the 1st decade of the 21st century “the 2 thousands”…since I called the years 2-thousand-one, 2-thousand-six, etc. This way, his 1st decade was 1930-39, this 7th 1990-1999, and his 8th 2000-2009. Either way, I’d say he spanned 8 decades, not 7…extra credit…very good!

B*A*K*E*R*S  D*O*Z*E*N

(1)  FOOB…the magic washday miracle!…and now
introducing new BOOF…it’s FOOB with bleach!…

(2)  Today, they probably film “deleted scenes” on purpose to include in a
movie’s DVD release…but back in the day, the director thought his work was
better without them, right?…interesting to see all these years later, but still…

(3)  Woody Allen said: Today we don’t throw
away our garbage…we make it into TV shows…

(4)  We’ve all had occasion to replenish…but did you ever plenish?…
you must have…it’s an old Scottish word meaning to supply, furnish, or fill…

(5)  New style among Baby Boomers…wearing 2 pairs of glasses at once…

(6)  So what the heck does the word semi-controversial mean?…that there’s
controversy about it being controversial in the first place?…or something else?…

(7)  Feel like there are bees living inside your head?…let ’em out!…

(8)  Nothing I read all week made more sense than this sign on a truck:
IF YOU CAN’T SEE MY MIRRORS, I CAN’T SEE YOU…

(9)  Are we really getting that stupid?…if you have to tell them not
to eat their earbuds, I’d say yeah…but talk about mixed messages…

(10)  Some cool names in the September baseball call-ups…that’s not
how New Mexico spells it, but so what?…also, welcome Didi Gregorius
from Holland, Jurickson Profar* from Curaçao, and Tanner Scheppers…

*Hit home run in his first Major League at bat Sunday for the Rangers…

(11)  If you love someone…set them free…and if
they don’t come back, call them when you’re drunk…

(12)  Ever notice…workplace shootings never
seem to happen at gun shops…I’m just sayin’…

(13)  This presidential campaign will be nasty, but nothing like 1800,
when challenger Thomas Jefferson called incumbent John Adams…
a hideous hermaphroditical character, which has neither the force and
firmness of a man, nor the gentleness and sensibility of a woman…yeesh!

POUTINE-ON-A-STICK

It’s a true fact that the worst monster movies still had great trailers and posters…Reptilicus is the perfect example…I can still remember ogling that ad when I saw it in the papers in 1961. Despite the cheesiest monster this side of the Giant Claw, this is still a decent movie, well-plotted and suspenseful…until you actually see the Beanie-and-Cecil-eque puppet monster. Worth hunting down the Danish original version, which actually has the creature flying!

But popular enough to spawn an 8-issue series of comic books…albeit by weak sister Carlton, which would latch onto anything that moved. And watch for clips on episodes of The Beverly Hillbillies, Green Acres, and The Monkees. Gotta admit, that “nature” line from the trailer is a doozie…I mean, can it do that?

POUTINE-ON-A-STICK EXTRA

Last week I pointed out that one of the things that means the opposite of what is says is: It’s nothing personal. Well, at least this kid took it all in stride. This approach sounds so darned reasonable, but is it really? I say no…I say there is no way to “even things up” that’s fair to everyone. And not only is it unfair to Demias, it’s also unfair to the kid who might otherwise have figured out a way to stop him. That’s the whole point of athletic competition…and competition in real life, for that matter. BTW, this was from last year…he’s now in the 7th grade and the restrictions are off…so he can play some football the real way…

Posted in Uncategorized | Leave a comment

stolf’s blog 8/27/2012…and how!

The White Sox’ Adam Dunn is having a season that’s being described as “Ruthian”…how can that be?…dude is only batting .205. Yes, well, that’s still some 40 points higher than last year…but what’s Babe-esque about the whole deal is that Dunn is currently leading the majors in home runs, strikeouts, and walks…and the only player ever to do that was the Bambino…in 1923, 1924, and 1927. Now with respect to strikeouts, he’s still on a pace to beat Mark Reynolds’ single season record of 223 by 10 or so…a few months ago it looked like it would be much more than that, but over 162 games, things tend to even out. For example…

8 times a player has finished the season with a Strike Out Average of over .400…minimum 100 strikeouts. The record is .437, Melvin Nieves of Detroit in 1997, 157/359. Now I divide strikeouts by at bats…some prefer plate appearances. My reasoning is similar to excluding walks as at bats for the regular batting title…if they’re not giving you anything to hit, only a doofus could swing and miss…you don’t swing in the first place…or in old school terminology, “offer at the pitch.” Now 60 games ago, Dunn’s SOA was an eye-popping .467…it’s evened out, now standing at a mere .408.

So the question is, why hasn’t Cody Ransom’s SOA evened out? 60 games ago, it was .469…today is .463. Well, probably because the Brewer infielder gets only about half the ups that Dunn does…and he’s just “better” at striking out, pure and simple. Altho the watch is on…he’s struck out only 99 times, 1 shy of my arbitrary cutoff point for the SOA record. BTW, if you lower that level from 100 to 50, Dave Nicholson holds the top 2 spots 55/113 for .496 in 1960…and 76/113 for .439 in 1962. In his 7 years career with the Orioles and White Sox, he was the certified God of Whiffs, with 573 career K’s for a SOA of .404…also believed to be the record. Until this recent crop, there’d been literally nothing like him.

And also BTW, as with most single season records, the minors beats the majors…and that would be Jermaine Swinton’s SOA of an astounding .538…182/338 with Asheville in the Midwest League in 1992. Well, that’s the best I’ve found…top it if you can…

B*A*K*E*R*S   D*O*Z*E*N

(1)  Back in the day in baseball, a relief pitcher was called a “fireman”…
the starter would pitch till he got in trouble, and the reliever would then,
and only then, come in to “put out the fire”….relievers weren’t
regularly scheduled…as set-up man and closer…as they are today…

(2)  The worst part of writing is the paperwork…which is why blogging
works out nice…altho I do always have to have a hard-copy… 😉 😉

(3)  Never heard it called that before in sports…the PUP list…
Physically Unable to Perform…or should that be PhUTP list?…

(4)  Guacamole chips?…well, potatoes are good enough for the
likes of me, but to each his own…sez me…and God bless…

(5)  Garfield the cat recently said: The world exists
for my amusement…this must be an intermission…

(6)  If somebody murders you, it will almost certainly be a person of
your own race…according to government statistics, white on white
murders, 86% of the time…black on black, 94%…food for thought…

(7)  In naming animals, -odon refers to “tooth”…most are extinct…
dinosaurs Trachodon and Iguanodon…reptiles Dimetrodon and
Pteranodon…giant shark Megalodon…and saber-toothed cat Smilodon…
2 that are still with us are the shrew-like Solenodon, found only in Cuba
and Hispaniola…and the Tuatara, also known as the Sphenodon,
resembling a lizard, but different enough to have its own classification…

(8)  A vehicle with an “electronic back-seat-driver”?…
telling you what’s wrong with the way you’re driving?…
with today’s nanny-state mentality, wouldn’t put it past them…

(9)  Thomas Mann wrote: “Man was a result of God’s curiosity
about Himself”…certainly ties in with “made in His Own image”…
as opposed to mankind being “something completely different”…

(10)  Phyllis Diller said: I want my kids to have
everything I didn’t have…then I’ll go live with them!

(11)  This is from the Yahoo Sports website…double standard?…your call…

(12)  Mark Twain opined that the nice thing about
telling the truth is that it’s easier to remember…

(13)  Arab proverb…popularized as I recall by Truman
Capote…The dogs bark, but the caravan moves on…

POUTINE-ON-A-STICK

I liked drawing pictures of cars as a kid…now you can mess with the image on the computer…as well as design names and logos for dopey “letter” cars…

POUTINE-ON-A-STICK EXTRA

You hear all about mermaids…but according to legend, there where mermen too…collectively known as merfolk…the jewelry on the left, that’s a merman with the green tail…

Posted in Uncategorized | Leave a comment

stolf’s blog 8/20/2012

Saw a cable news talking-head lady referred to in the paper as “openly gay”…so what other kind is there? Well, closeted, obviously, but is there anyone today that a responsible journalist would describe as “gay, even tho they’ve never publicly admitted it”? Don’t think so, my friend. Easier to pass judgement on figures from the past…Liberace was, Abe Lincoln wasn’t, etc. And it sure is interesting how it’s OK to be gay, but not OK to wonder if someone is. Would it be out of line to suggest that straights tend to answer: “What difference does it make?”…where gays would answer: “I wish.”

For for the record, most of those actors who adopted a swishy persona back in the day really were homosexuals…Paul Lynde, Charles Nelson Reilly, Alan Sues, Rip Taylor…one exception being Louis Nye, for whom it was just a put-on. Harvey Korman is a question mark, meaning he never openly said one way or the other…web opinion actually leans towards not. I believe the rule today is, if they don’t say so publicly themselves, you have to assume not…

And Jack Benny of course was straight…it seems that the thespian tradition of the effeminate yet hetero (or as my spellchecker keeps insisting on spelling it, “heater”) male has gone by the boards….think Gale Gordon, Jonathan Harris, et al….or are they just “fussy”? But even Benny played it for laughs…when you-know-what was decriminalized in English in 1967, he quipped: “They legalized my walk!”

But it’s also interesting to observe that nobody would ever say “I am not an ax-murderer…not that there’s anything wrong with being an ax-murderer”…whereas…well,  you get it…

B*A*K*E*R*S   D*O*Z*E*N

(1)  Things That Mean the Exact Opposite #27: “It’s nothing personal“…

(2)  Do not be dismayed when the government approves
of an illegal activity, in this case immigration…perhaps
next they’ll approve of something illegal that YOU like to do…

(3)  …altho it is a puzzlement…illegal immigration
gets a pass…but illegal parking doesn’t… 😉 😉

(4)  Mowing his lawn, Cool Daddy wears a
t-shirt that reads Do Not Resuscitate…

(5)  …the rest of the time, he’s old school, wearing t-shirts
that don’t say anything at all…he calls them “mutes”…

(6)  Women will get angry if you say they’re illogical…they also get
angry if you call them logical…well, that’s because…oh, never mind…

(7)  I would say that, in general, setting a good example is vastly
overrated…altho recently, I was delighted to discover it can work…

(8)  A study of past Olympic athletes found that bronze medal winners were
happier on the whole than silver winners…the silvers wondered why they
didn’t win the gold, while the bronzes were glad to not have finished 4th…

(9)  …that sounds like a joke, but its true…but why would they even
do such a study in the first place?…I’ve been saying this for years:
there isn’t enough in the world for everybody to have something to do…

(10)  Guess what?…Responding to rudeness with rudeness…is rude!…

(11)  Since you can’t believe anything they say,
vote for the candidate that says the least…

(12)  The new campaign rhetoric: “My esteemed opponent…is unhinged”…

(13)  Why do they let crazy people write newspaper columns?…
one recently said that saying Sikhs aren’t Muslims…is anti-Muslim…

POUTINE-ON-A-STICK

Racial sensitivity is getting so out of whack it’s hard to fathom…case in point: The Bank of Canada recently rejected this design for the back of their $100 notes. A focus group thought that the lady peering into the microscope looked too “Asian.” Now a few years ago, this might have been construed as anti-Asian…I mean, imagine objecting because a drawing of a person looked too “Black.”

But the thinking today is twofold: it plays into the “negative” stereotype that Asians are smart…and also, other bank notes don’t have other ethnicities to balance out the diversity. Do you see an Asian lady here? Sorry, I just don’t. Oh yeah, and some also said the color of this bank note was racist, so help me. I will say this: it sure is a sloppy design overall, but that’s the preference these days…

POUTINE-ON-A-STICK EXTRA

And speaking of bees in bonnets…some are objecting to this Joe DiMaggio stamp because they think it looks like he’s batting left-handed, and of course he was a righty. If you notice where his hands are placed on the bat…right hand above left hand…this is exactly correct for a right-handed batter. When I first saw this picture, I naturally assumed he had just hit the ball and this was his follow-thru…again, the placement of the hands tells you that instinctively.  The trouble is, the bat is in an unnatural position…this was explained as artistic license. In any event, the Postal Service is not going to change it, which sounds like the sensible course to me.

Posted in Uncategorized | Leave a comment