Peanut Butter Sandwiches

Just the facts ma'am:

900 total Peanut Butter sandwiches of varying ilks

600 Peanut Butter and Jelly - PBJ

390 Peanut Butter and Banana - PBB

400 Peanut Butter and Pickle - PBP

250 Peanut Butter, Jelly, and Banana - PBJB

150 Peanut Butter, Jelly, and Pickle - PBJP

200 Peanut Butter, Banana, and Pickle - PBBP

20 Peanut Butter, Jelly, Banana, and Pickle - PBJBP

Remember that any grouping is included inside a larger group.  Such as the 250 Peanut Butter, Jelly, and Banana, is by definition Peanut Butter and Jelly so included in that group of 600.  Think in terms of a Venn diagram.

Now the question is:  How many PB sandwiches are neither Jelly, Banana, or Pickle?

And we're off:

Start with the center of our three circle Venn diagram - 20 PBJBP, which means there are 180 PBBP, 130 PBJP, and 230 PBJB because each of these Venn intersections contain the 20 PBJBP.

Moving outward into the larger circle sections of our Venn Diagram we get 170 PBJ, 70 PBP, and 10 PBB.  Now to compute the remaining Peanut Butter sandwiches we subtract all these sections from our initial 900 sandwiches.

900- 20 - 180 - 130 - 230 - 10 - 70 - 170 = 90 remaining PB sandwiches.

Alien Challenge: Save the Earth!!!!

An energy being from Alpha Centauri comes to your home to test Humanities intelligence.  IF you answer correctly, humanity will become part of a large intergalactic federation. If you answer incorrectly, the alien will shroud the Earth in perpetual darkness.  Here's the problem:

1.  Consider an integer N that is greater than 1.

2.  Consider the integer M, which is the square root of N.

3.  Given that M is the sum the digits of N, what is N and M?

Hint:  Only one value of N can satisfy these properties.

Solution to July 20th's Brain Teasers

First of all the Power of Two Proposal:

I am going to just consider the powers of 2 in order.  2, 4, and 8 do not qualify because they are not multi-digit integers.  16 is disqualifies because 6 is not a power of 2.  32 is disqualified because 3 is not a power of 2. 64 is out because of 6 again.  Now we get to 128.

1 = 2^0
2 = 2^1
8=2^3
And 128 = 2^7.  Obviously this is the smallest, but I wonder what the next one is.

Tom, Dick and Harry Food Venders.

Remember Tom shows up every other day.  Dick every third day.  Harry every 7th day.  They were all together on April 11.  There are many ways to skin this iguana but one can just consider 2,3,7 as multiples and find the Least Common Multiple of all which is 42.  Hence they will all be together 42 days from April 11, which is 23 May.

High School Reunion - 25 years

Last night I attended a special event - the 25th reunion of Ellicott High School's 1988 class.  Sue Smith and I were the only teachers there, which was a shame because there were some very special former students in attendence.

But I get ahead of myself.

1988 - I was 37 years old.  It was my fourth year of teaching in Ellicott, a small town on the plains of Colorado, which was destined to become the model for East Plains, the town in my Bonnie Pinkwater mystery series.  We were in a new building, across the street from the original school, which once housed all thirteen grades of this tiny school district. I was there on the day when the local chapter of the Masons performed their arcane ritual involving oil, salt and wheat on the cornerstone of the new school, which would hold the 7th thru the 12 grades. I knew every teacher and every student in the halls (the 1988 graduating class would have 45 students), including Susan Smith who would become my lifelong best best friend. Together, the two of us would comprise the entire math department.  

In 1984, I followed, Tom McCombe (the new principal and and an old friend) to the school, thinking I would work there for only one year then move on to a bigger school district, one which paid more money, had more programs.  I was broke, newly divorced, had started smoking again.  My first day of work there was a cow standing in my parking place. The original school was run down, 30 miles east of Colorado Springs in what had to be considered the desert.  The populous were ranchers and farmers.  I grew up in Philadelphia population 2 million.  Ellicott had tornadoes and dust storms, for God sake.

By 1988, I couldn't imagine working anywhere else.  The students who would graduate that year, I had watched become young men and women since my first year in 1984.  I had learned to love them, cry with them ( I followed one girl into the bathroom and sat down on the floor next to her as she cried her eyes out. I imagine such behavior would get me arrested today. She would be at the reunion).  I wrote them a song and sang it at graduation - it was my first and wouldn't be my last.  I knew what was happening in the lives of all my coworkers - the problems with their spouses and children, the secrets they entrusted me with, the days when they needed hugs.  Many of them brought their own kids to the school and these would sometimes end up in my classroom. We would commiserate over what was happening at school versus what was happening at home.  Don't get me wrong.  The money was still atrocious. I was always broke, needed a new car, new clothes.  But I loved coming to work.  I stayed for 18 years

Last night I saw these same teenagers again, except they weren't teenagers anymore.  They were older than I was when I was their teacher, most of them now 43.  Many had gray in their hair and beards.  A few were grandparents.  Many no longer resembled the kids in the yearbooks and my memory.  All were a joy to look upon as they told me what they had been up to in the 25 intervening years:  engineers, plumbers, airline attendants, ranchers, general managers of companies large and small.  What's more they remembered me.  We laughed as we recalled things which transpired a quarter of a century ago.  They introduced me to their spouses.  And before the night was over they said the words which were water to my soul.

"You made a difference in my life." 

July 20 Brain Strain: The Powers of Two Proposal

Beezer Wentwistal asked Zenobia Tightbottom (from the famous mathematical family of Tightbottoms) to be his wife.  She answered his proposal with one of her own:

"I will marry you if you can solve a math challenge.  I am thinking of a multi-digit integer N that is a power of 2.  Moreover, each digit in my integer N is a power of 2.  What is N?  If you cannot answer I'm afraid I cannot consider you a viable mate since I require intelligent offspring."

Can you help Beezer marry the love of his life?

Camping in the Back Yard Part 2

Having frozen and been revived by my wife at the end of snow-drenched May, I refused to be deterred.  I would take this camping experience to the next level.  I would bring out the big guns.

Two years ago, on Black Friday, the day after Thanksgiving, I had gone to Dick's Sporting Goods to get a sleeping bag and tent because I was going to backpack into Rocky Mountain National Park with a pair of my teacher friends.  They were going for the fly fishing.  I would write and hike--I did end up writing a few chapters to Radical Equations, my latest Bonnie Pinkwater mystery.  The tent was a piece of cake, a one and a half pound backpacking tent that was little bigger than a coffin.  The sleeping bag was another story.  Dick's had a number of spiffy bags on sale but the one that finally caught my eye was rated for forty below.  That's right campers, forty degrees below zero.  With this mother puppy I could conceivably sleep in a snow drift.  Truth was I had no intention of camping anywhere near a snow drift.  I was heading into the mountains in the dead of summer, first Rocky Mountain National park then a campground just outside of Leadville.  In both cases, the bag would prove to be just too damn hot.  I ended up just laying it across myself and even then the darn thing was an oven.

But with the winds blowing 50 mph in my back yard and three inches of snow on the ground, AS GOD AS MY WITNESS, I WOULD NEVER BE FROZEN AGAIN.

Now the accouterments were waiting - a four-man cabin tent with an eighteen inch thick air mattress, and a big hunker flashlight - when I boldly walked ten paces out my back door.  It was cold, sure, and got colder as I took off my warm clothes and wiggled into my snug sleeping bag.  Except for my nose, I got warm in a hurry.  After finding a way to bury my chilly nose in the bag, it was time to get comfortable and settle down for a long winter's nap.  That's when things got complicated.

You will never get me to admit to being chubby but I had gotten bigger than when I last used the rated-forty-below sleeping bag - things were a bit snug.  I sleep on my side and I just couldn't come to an understanding with this bag to allow me to turn sideways and still have my nose not turn into an icicle.  First I tried to turn in the bag.  It is a mummy, so the feet portion is considerably smaller than the rest.  The overall effect was that my body only turned with great difficulty. and then I discovered that the flap would no longer reach my nose and it was growing frigid.  With an equal amount of difficulty, I returned to my original position.  I halfway convinced myself that I would just sleep on my back. I lay there waiting to sleep.  Minutes past that felt like hours.

Then an idea came to me.  Why not turn everything, me the bag, the necessary flap, the whole kit and caboodle.  Easier said than done.  Before I go into the grim details of this next escapade, there are two things that need to be said.  Thing 1: I wear glasses.  Trifocals that allow me not to be blind as a naked mole rat.  These were laying on the floor of the tent next to the flashlight.  Thing 2: The air mattress, thick as it was, was only a single, not as wide as the bed in my bedroom only thirty paces away. Me and my sleeping cocoon filled this surface area quite nicely but there wasn't much room left over for doing the tango.  Keeping the necessary flap in place I tried to turn.  The slicky bag wanted to stay in place - I believe this is called inertia.  This would never do.  Idea number two.  From the inside, I would grab hold of the bag and kind of hop/roll onto my side. Believe it or not this worked marvelously - for about a second.  I launched myself off the mattress into free fall.  Still twisting sideways, I tumbled onto the flashlight turning it on, which was handy because I was in kind of a fix.  I had gotten myself tangled up in the bag, kind of half turned but not all of me.  My feet in the smaller section of back were going one way while the rest of me was turned ninety degrees.  And I was face down on the cabin floor, the flashlight shining into my eyes.  Then an awful thought presented itself to my bedazed mind.

Where were my glasses?

After an eternity, I disengaged myself from my captor sleeping bag and tried to gingerly roll.  I found my glasses.  At first glance they seemed relatively unscathed.  They fit my face - mostly.  Then I looked around the flashlight lit tent.  Something wasn't right.  The big red writing on the tag that told of how to care for the tent fabric was indecipherable.  And now the glasses weren't feeling so right on my now cold nose.  My hands crept to my face and I realized the awful truth.  One of the lenses was missing.  And I was maybe too blind to find it.  Oh my God, did I shatter it when I fell?  Was I, even now, walking on the broken shards of my trifocals?  Like a madman I tossed aside my rated-forty-below sleeping bag and felt around the edges of the air-mattress.

I found the lens.  It wasn't broken.  But I was.  In my underwear, holding my lens I stumbled back to my house.  My wife was waiting.  She took one look at my glasses, part on my face and part in my hand, and gave me a tender hug.  Have I ever mentioned that I have the best wife in the world?  She took me to my bed, tucked me in and crawled in beside me.  She even helped get my nose warm.

A Day at the Doorly Zoo

I had been reading about this Omaha, Nebraska zoo for over two years.  It had a reputation for giving the one in San Diego a run for its money and for the most part it lived up to its rep.  I had just gone to the zoo in San Diego nine months previous and am a huge fan of our own zoo (Colorado Springs) up on Cheyenne Mountain, so I reckoned myself a bit of a zoo connoisseur.  First of all, this bad boy is big, so if you go get ready for a lot of walking, although there is a train, a tram and an overhead sky ride, but for my money to be really savored, a zoo needs to be walked.

Things I liked:

They have a night area.  There's something sooooooooo cool about walking around in a place that perpetually dark.  I'm not talking about dim, it is flat out dark in there.  Obviously, this pavilion houses creatures that prefer the dark and if you're like me, you think bats.  I LOVE BATS.  I LOVE BATS.  There I've said it.  They had six species of bats, including (drum roll please) vampire bats.  The little buggers were even lapping up blood.  How cool is that!!! But my favorite was the giant fruit bats.  These guys had wing spans of like four feet.  Now that's a bat.  Oh yeah, and Naked Mole Rats.  Who doesn't like them?

Lots and lots of bears.  What's not to like about a bear.  Every time I see one I think of the folk song, 'Mama's Taking Us to the Zoo Tomorrow.'  "Bears walking round with their woof, woof woofing."  Polar Bears, Brown bears, Grizzly bears.  Cool beans

Tigers.  One tiger roared over and over again and paced around it's giant enclosure.  Loud, impressive.

Lions.  It must have been some sort of day care/school day because there were a ton of kids running around that day and one particularly, shall we say expressive young girl, insisted on shouting, "Wake up, wake up you."  After a minute of this abuse, the lion opened one eye and fixed it on the girl as if to say, "Please come a little closer, darling, so I can show you what waking up really looks like."  The little girl was appropriately cowed. And one mama lion had four baby lion cubs.  All spotted and cute.

They had a Komodo Dragon.  I love these guys.  They look like they just want to bite you with their nasty bacteria infected mouths.

The Jungle River pavilion was extra cool.  Can you say pigmy hippo?  This little guy had his own river and looked like I feel when I'm on my first day of vacation in Florida.  This place even had an albino Alligator.  Huge, white, with a terrific overbite.  We walked on rope bridges, along a winding river, and looked down on very cool monkeys from the tree canopies.  It was even appropriately hot and sultry.

Bird Sanctuary - a giant enclosure, I'm talking massive.  Pink birds, striped birds, huge birds, tiny birds, birds in the trees, floating on a river, flying from branch to branch, AND NOISY.  It seemed only fair.  This was their turf.  They should be able to sound off as much as they want in their own home.  If I didn't like it, I could leave.

Orangutans.  Not much to say except one young guy just hung there with his legs spread as if to say, "Ladies and Gentlemen, this is my penis."  I recognized something of myself in his demeanor.  This area also enclosed one of the most beautiful silver-backed gorillas I had ever seen. Magnificent!  He was just regal in his large run.  a small gibbon braciated from branch to branch like it took no effort.

Of course there were giraffes and penguins, rafts of monkeys, even a butterfly pavilion.  But I'm not going to go on much longer.  You probably already got the picture.  I had a the best time I think I've ever had in Nebraska.

Camping in the Back Yard

Okay, here's the thing.  I am retired (even more so now but that is grist for another post).  I am planning trips galore: Mexico, Olympic National park, California, Florida and even a few more.  My wife and I will stay in hotels, on trains, in hostels, so it wasn't a great leap to consider camping.

Now, I have no shortage of tents, from a one-man coffin tent, to two and three-man domes to a big old cabin tent that supposedly sleeps four.  It also needs to be said that my wife was less than enthusiastic when I broached the subject of camping in say, Yellowstone or Zion.

Sooooooo, I suggested that I could make our cabin tent extremely homey, perhaps with the addition of an air mattress that I would gladly fill up every time we went camping (I being the rough and tumble outdoors-man would not need such frilly additions).

Which brings me to last Monday.

With an energy bordering on mania, I purchased a cool air mattress and pump (not an electric one but a hand pump.  I figured, "I can use this baby no matter where I am, even if I can't get to a electric outlet").  Then I went down into my basement and brought out to my back yard the impressive, the gigantic, the hopefully homey CABIN TENT.  I approached the setting up of this monstrosity with a zen-like calm and with just one more trip to a hardware store (I needed some more guy-rope to secure the corners) I set about my task.  I don't want to brag, but I believe I did splendidly. Not only did I calmly figure out the slip knots needed to snugly tie down the upright and corner poles, but when I ran into challenges (one of the cross-beam poles in the roof refused to allow itself to be elongated easily), I didn't rant and curse (I am after all, a spiritually advanced individual), I doped out solutions.  Inside of an hour, I had the beautiful structure standing.

Next came the air mattress.  It was here I had my first inklings of doubt.  After two hundred pumps, my wonderfully thick air mattress (it promised to be a full 18 inches in depth) still wasn't fully inflated.  Maybe the electric pump would have been a good idea.  So, it goes. Eventually, I got the darn thing up to its potential.

For those of you who actually live in Colorado, you might at this juncture be thinking. "Hey wait a minute.  Didn't some bad weather, snow and high winds, come in last Monday?"  If this was your thinking, you were absolutely correct.  Before I finished inflating the magnificent air mattress, the wind had kicked up to about 40 mph.  However, I was undaunted.  After all, I had tied down the tent quite expertly.

By the time evening rolled around, it had snowed about 4 inches.  But my enthusiasm would not be dampened.  My wife looked at me like I was out of my mind.  "Do you really mean to do this."  I put on my best outdoors-man face.  "Of course."

When I couldn't delay any longer I headed out to the tent.  I had camped a few summers ago in Leadville, Colorado, which even in the summer, gets very cold at night, so I know that a closed up mummy sleeping bag was just too darn hot, so I had chosen to open my sleeping bag as a thick blanket and take my repose in this manner.  Let me, at this juncture, say that I was very comfortable on my inflated mattress and at first even acceptably warm.  However, things change.  Two o'clock in the morning I woke feeling somewhat chilly.  It wasn't like I was going to die or anything, but there was no getting over the fact that I was cold.

No problem.  I'll just zip up the blanket into a nice warm downy sleeping bag.  In the light of a flashlight, I realized the terrible truth.  Because I wanted to use a blanket and not a sleeping bag, I had chosen the one sleeping bag that had a broken zipper.  Still, I wasn't ready to give up. Surely, I could position myself beneath this excellent blanket and find the requisite warmth needed to fall back into the arms of Orpheus.

An hour later, I gave up.  Chilled to the bone, I made my way back into my house and my ordinary, dull, but warm bed.  My wife might possible be one of the nicest folks on the planet Earth. She never said one reproachful word, but merely hugged me until I stopped shivering.

The next morning I informed her that I was not ready to completely throw in the towel.  With a new sleeping bag, I would brave the snow and wind (which pummeled my poor tent the next day at 60 mph) the following night.

This next adventure will be the subject of my next post.  I will say this.  Things went from bad to worse.  

Answer to this week's puzzles.

Dear Puzzlers,

First of all the answer was yes, you can fit the 70 cm sword.  I'll congratulate the winners on Facebook but for now the solution.  The box was 30cm X 40cm X 50cm.  We will solve by a repeated use of the Pythagorean theorem.  First the bottom:

30 squared + 40 squared = hyp squared

900 + 1600 = 2500 --> hyp = 50

Use this in a second application of the Pythagorean theorem:

50 squared + 50 Squared = large hyp squared

2500 + 2500 = 5000 --> hyp = 70.5cm  THE SWORD WILL FIT YAY!!!!!

Now the first two answers (the missing integers)

As we recall we had some info regarding the product and sum of 5 one-digit integers (product = 2520, Sum = 30).  We know two of the integers are 8 and 1.  5 must be one of the numbers since 2520 ends in 0.  Subtracting from 30 we get 16.  Which means we get 8 and 8 or 9 and 7, but the numbers must be different so 9 and 7 it is.  Therefore the numbers are 1, 8, 9, 5 , 7.

If we allow the numbers to be the same the only other choice is 8 and 8 BUT the product is not 2520 so the answer to the adjunct problem is that we get no additional answers.

1, 8, 9, 5, 7 are the only solutions.