A Numbers Puzzle

How many jelly beans are in the jar?  It is a classic head scratcher.  Today I’m going to talk about how I approach these puzzles and share some numbers data because numbers are fun!

How Many Dice are in the Aquarium?

This was the challenge put together by the local game store.  Over 800 people guessed.  Do you have a number in mind?  It’s okay, I’ll wait.

Ready?

 

 

Here is a breakdown of how everyone else guessed.

Click on it for a bigger more readable image.

My own guess was 4780.

Here is how I reached that conclusion.

First of all, always try to get more information!  I knew this was a yearly challenge so I went back and looked at the past two years.

Here was the previous year picture.  There were 2,813 dice in the aquarium then.

That is a huge data point and potential advantage when making a guess.  I drew in some lines on the current challenge.

We now know a big triangle has about 2813 dice.  We can clearly see two big triangles in the current aquarium, but they have some overlap.  The challenge is to figure out how many dice are in the intersection of the two triangles so we can math it up.  Triangle 1 + Triangle 2 – Intersection = # of dice in aquarium.

Or

2813 + 2813 – intersection = ???

By drawing a line straight down in the middle of the intersection, we can make two right triangles.  That makes the math a bit easier.  Then we need to start counting.  I counted length and height for both the big triangle and the little intersection triangle.  My count of the big triangle was 22 dice wide by 12 tall.  We don’t need to worry about the depth because it is all the same depth.

From the previous year, we know that 2813 dice occupied 22×12 triangle.  Convert that 22×12 triangle into area (multiply height x base and divide by 2).

22 x 12 / 2 = 132 area.  2813 total dice divided by area (132) = 21.31 dice for each cube of dice volume.

Now count the little triangle.  I got 10×4.  Each little triangle would have an area of 10×4/2 = 20, but there are two little triangles so it is just like a rectangle.

We now have enough information to make an educated guess.

The intersection is 40 area x 21.31 dice per area unit = 852 dice in the intersection.

2813 + 2813 – 852 = 4774 dice in the aquarium.

There is one more thing that we can do to get a competitive advantage.  That is look at everyone else’s guess!  By finding the biggest available range of non-guesses we can maximize our odds of winning.  If someone guessed 1 and someone else guessed 3, you wouldn’t want to guess 2 and lock yourself to a single number.

Since this challenge was posted publicly to Facebook, it is really easy to grab all of the other guesses and put them into a spreadsheet.  I used a free tool called FacePager.  It lets you quickly dump all of the posts, comments, etc. from a public page into a spreadsheet.  Then you can massage the data as you like.  For instance, the simplest way of finding a big gap between guesses is to create a second column next to the original column.  Do a simple A2-A1 formula and extend it all the way down the second column.  The bigger the number, the bigger the spread in guesses.  Look for the biggest spread near the estimate we arrived at above (4774).  In my case, someone had already guessed 4779, so I simply did 1 more than that at 4780.  That bought be about 20 possible numbers to win.  All of that guesstimating improved our odds of winning from 1/800 or 0.125% to about 1/100 or 1%.  That doesn’t sound like a lot, but it is nearly a tenfold increase in the likelihood of winning.  Not to shabby for a few minutes of work!

So there you have it.  Now that you know my secret, I’ll have to off you.

Oh, you’re asking how many dice are actually in the aquarium?  I don’t know yet, some unlucky bugger is still counting them!

Some Pictures from Spring

I have some more interesting blog posts in the works, but for now here are some pictures from our lives.

Here I am firing up the grill on the first nice day of Spring.  I’m also imparting some wisdom to Frugal Boy who is perched on a five gallon bucket.

Later that night, Frugal Boy put together his very first banana boat.

A few days ago, we voted in a local election.  Our mayoral race was not close, but the neighboring town was too close to call with only a 7 vote difference between candidates with 35 absentee votes still waiting to be returned.

Also on the ballot were school board members, the folks responsible for 62% of our property taxes.  They probably have the biggest ratio of taxes to media coverage of any elected official.

Frugal Girl tried out a smile for size.  It is hard to believe that she is almost a month old.

Frugal Boy and I went to see the circus.  I don’t think he’ll be running away and joining them anytime soon.  It was a bit of struggle to keep him interested.

Odds and Ends for December

The weather has been frightfully cold.  I know because I spent 20 minutes changing a flat tire this morning in a parking lot.  Before you travel for Christmas or New Years, double check that your spare tire is in good shape, a jack, and tire iron are included and in working order.  It is also a good idea to have a blanket in the car.

On a different topic, Shae and I enjoyed watching the movie The Company Men, starring Ben Affleck and Tommy Lee Jones.  The movie follows several white collar workers who face downsizing during the 2008 financial crisis.  It offers a great cautionary tale of living above one’s means.

Finally, after three and a half years, we have furnished all three bedrooms in our house with mattress sets and frames.  The last acquisition was a $85 Craigslist bed frame made by the now defunct Cochrane furniture company.

Odds and Ends

Summer is cruising by and we have been keeping busy.

I read a great murder mystery book by an up and coming new author.  Okay, the book was penned by my sister AND I got a copy for free, but I still enjoyed reading it.

Frugal Boy has finished up his summer reading program and now has a bag full of coupon goodies.

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After many months of trying to hawk the Microsoft Surface tablet that we won in a cereal box sweepstakes we finally found a buyer and unloaded it for $325.  Then the buyer had problems registering it and was upset so we found a happy resolution at $225.  Whatever, we found $225 in a cereal box.  Color me happy.

In less drama filled gadget news, Shae’s Fitbit wristband doodad gadget had started to peel and bubble around the display.  She wrote in and asked if there was something that she could do to fix it and they just sent her a brand new one.  When she asked if they wanted the old one back, they said no, just toss it.  Guess who has a ‘new’ Fitbit.  😀

We had a pizza party and movie after Frugal Boy got his 100th potty training sticker.

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We have also been playing with ‘blocks’ (Lego Duplos) a lot lately.  I gave Frugal Boy all of the parts to build the fire engine and this is what he came up with on his own.

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It has been hard to sleep at night because of the heat and humidity so people have been getting naps in wherever they can.

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The babysitter was shocked to find out that we don’t have air conditioning.  What I didn’t go into detail about was that we are saving up money for a downpayment on an investment property.  If we end up pulling the trigger, I’ll do a more in-depth numbers post, but for now, here are a couple of the properties that we have taken a look at.

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I picked up what should be the last load of lumber for rebuilding our front porch.

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The 23 boards above are for the skirting that goes around the bottom of the porch.  I stopped updating my porch rebuild spreadsheet, but based off where I left it and a general idea of how much I’ve spent since then, I figure this whole project will come out to around five grand.

I decided to get cutesy with the skirt design and stole inspiration from here.  It wasn’t too hard to recreate.

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The treated lumber that I picked up from Menards has been utter crap.  They looked alright when I picked them from the stacks, but the high humidity has been causing all sorts of grief.  Hopefully, they won’t completely twist, split, shrink, or crack when all is said and done.

Our garden has been outputting daily vegetables.  Japanese beetles have done a number on our bean plants, but tomatoes and carrots have been doing well.

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The Rising Tide of Protectionism and Nationalism

2016 is shaping up to be one for the history books in no small part to yesterdays referendum held in Great Britain.  In case you were unaware, the UK citizens voted in favoring of leaving the European Union.  The ‘Brexit’ or British Exit was not expected to happen by most think tanks and caught the rest of the world off guard.  Supporters of Brexit believe that it will help to ‘Take Back Their Country”.  Does that sound slightly familiar for USA citizens?  It should, the Republican nominee for President uses a very similar “Make America Great Again” slogan.

The growing popularity of nationalism, both here at home, and abroad is a step in the wrong direction in my opinion.  Most supporters of such a mentality favor decreased immigration, more isolationism, and a feeling that their culture, country, land, people are the best.  The last time that dozens of countries had this boisterous attitude, there was a colossal world war.

The opposite of Nationalism is Globalism.  In Globalism the borders between countries blur or disappear altogether.  If you are a Star Trek fan and like the idea of living in the Star Trek universe, then Globalism is for you.  The European Union was founded with the ethos of Globalism.  The thought was that if all of the European countries were united together in trade and citizens could freely move about between countries, then another catastrophic war could be avoided.

In the Brexit case, the primary motivator was immigration.  The civil war in Syria has created millions of refugees.  These refugees aren’t malevolent individuals.  Sure, there might be a few bad apples in the mix, but for the most part they are just families, or broken families, trying to get away from atrocities.  Part of the reason why Shae and I travel internationally is to learn about other cultures and peoples.  Men and women, infants and children, jobs and bills, for all intents and purposes they are the same as us.  Sure they may speak a different language, have a different skin tone, and may even worship a different god or no god at all, but they are still human beings.  Immigration is a wonderful thing.  Immigrants bring fresh blood to the workforce, new talents, creativity, a drive to improve, and a can-do-attitude.  By the second or third generation, they’ve been assimilated into the country and speak the language and have adopted the culture.

Adopting a xenophobic attitude, like the one that Brexit supporters or the Republican nominee, have adapted is short sighted and fool hardy.  Look no further than Japan, a deeply xenophobic country with tight immigration laws.  Like many developed nations, Japan’s birthrate has hovered at or below replacement rate for the past two decades.  Without young immigrants feeding into the Japanese economy, the native youngsters have had to sustain a larger aging population.  The result has been a stagnant economy for decades.

On the same side of the Nationalism coin, is Protectionism.  Protectionism is when a country tries to help domestic companies sell their products by blocking foreign competitors.  Governments pursuing a protectionism agenda can accomplish this by taxing foreign imports at obscene levels.  Both Donald Trump and Bernie Sanders have run their campaigns on a protectionism platform.  “Made In USA” is their rally cry.  Protectionism in my opinion is a poor grasp at turning the clock back 50 years.  America enjoyed a golden period after WW2 where every other major industrialized nation was in ruins.  Now, 65 years later, other countries have rebuilt and American companies face stiff competition.  This is the new reality, and there is no turning back the clock.  What these two candidates have failed to mention is that if Free Trade is sliced up with protectionist tariffs, the result goes both ways.  Trading partners such as Mexico, Canada, and China would be just as likely to retaliate with their own tariffs.  Nobody wins in a trade war, least of all consumers.

We all live in the same spot.  It’s time to start acting like it.

ApolloEarth1