Asked & Answered: 1.0
Posted on November 30, 2012 by CHC   ᐃ ᐁ

This is the first in a series of recreational math problems that I will be asking and then answering (to the best of my ability) in this space.  Hello?  Is anyone still reading this?

I have been doing recreational math for thirty-some years, but not so much lately.  I have had several articles published in Journal of Recreational Mathematics (which seems to have suspended publication several years ago).  But I still enjoy posing and then solving math problems of the type I present below.

• • •

I hate to carry pocket change.  [This is not a complaint — this is the setup to the problem.]  I hate it so much that I want to minimize the number of coins I carry when I have to make a cash transaction.  If I want to carry the fewest possible number of coins, defined as the average number of coins before and after the transaction, what coins should I start with?

Here are some assumptions that will help you solve the problem.  [Recreational math always involves assumptions.]  Assume that I have an unlimited supply of dollar bills and the only thing I care about here are the coins.  Assume that the only coins in circulation are pennies, nickels, dimes and quarters.  Assume that I can’t ask the cashier to convert one denomination to another as a side transaction (e.g., give her five pennies in exchange for a nickel).  Assume that the cashier makes change in a way that returns the fewest possible number of coins.  Finally, assume that it is equally likely for the transaction price to end in $.01, $.02, $.03, etc.  In other words, we want to minimize the number of coins we carry, on average, given some arbitrary number of independent, randomly-priced transactions.

Take as long as you would like to work on this.  The answer is given below.  Good luck.

• • •

Wow, that was fast.  Congratulations on your mental agility.  Now let’s see if you are right.

I initially guessed that I should carry at least one coin of each denomination.  The first case I studied was 2Q – 1D – 1N – 3P.  If you want to get rid of change, this is not a bad choice.  On average, you will unload 2.30 coins per transaction.  But your goal here is to minimize the average number of coins carried in your pocket or purse, and in this case the result is 5.85 coins (you carry 7 coins before the transaction and 4.70 coins afterward).

I suspected that this result could be improved upon.  Out of curiosity, I looked at the case where one carries no change at all and pays for every transaction with dollar bills.  This is in fact the best answer.  The average number of coins in your pocket in this case is 2.35. While you are gaining 4.70 coins per transaction, you are starting out with zero coins.

If you wonder why you accumulate change, this is the reason.  If you are like me, you offer only currency for 90% of your cash purchases.  For every ten currency-only transactions, you will come home with 47 coins (15 quarters, 8 dimes, 4 nickels and 20 pennies).  I had thought about verifying this result by counting the coins in my own change dish, but since I fish out the quarters and dimes to use in parking meters, my ratios would be off.

To close, let’s consider the effect of the “take-a-penny” dish next to the cashier.  If I carry no coins with me and use one penny from the dish whenever the price ends in 1 or 6, then the number of coins I accumulate per transaction drops from 4.70 to 3.90.  If I were also to “balance the books” by putting a penny in the dish whenever the price ends in 4 or 9, then I would accumulate only 3.70 coins per transaction.

So, here’s the bottom line — if you hate change, only carry currency, use the penny dish, and vote for conservatives.  Asked and answered.

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3, 13, 26, 47, 52 and 8
Posted on November 28, 2012 by CHC   ᐃ ᐁ

These are the Powerball numbers I would have selected but did not.  I expect to be vindicated (and two dollars richer than if I had played the game) come morning.

Thursday Morning Update:

The numbers were 5, 16, 22, 23, 29 and 6.   As expected, not a match to be had.

The total amount won in yesterday’s Powerball lottery was $711 million, $580 million of which was the six-number jackpot.  Since the participating states distribute only 50 cents of every dollar as winnings, this means the total amount spent on Powerball tickets since the last jackpot winner (eight weeks ago) was on the order of $1.5 billion.  Total revenue for the year is expected to be $5 billion.  For comparison, the organization CARE was able to raise $310 million in private support in 2011.  Food for thought, if not for the hungry.

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It’s Charley Again
Posted on November 21, 2012 by CHC   ᐃ ᐁ

Hello, it’s Charley again.  Back in the saddle here at the blog while the owner is on vacation. Lucky me.  He gets to eat turkey, stuffing and mashed potatoes while I sit in my quarters trying to clean out the crumbs in my keyboard.  No, I’m not going to eat the crumbs.

I’m going to take this opportunity to do something that this blog hasn’t done before, which is to print something interesting.  Obviously it’s about cowboys.   No one writes much about cowboys any more, because (as Neil Young noted) there just ain’t many of us left.

The reason is, cowboys can’t make a living wage these days.  As The Oregonian reported: “Hired livestock workers earn a little over $10 an hour, according to the U.S. Department of Agriculture.  In eastern Oregon, ranchers prefer to pay day wages — $100 to $150 — for buckaroos who provide their own pickups, horses and herding dogs.”

Times may be tough for cowboys, but then they always have been.  You may think that all we do is dude up and meet pretty women (click the image for details) but you would be as wrong as a six-legged mule.  And that is pretty damn wrong — just ask the mule.

Some of my old friends have taken to writing poems about the cowboy life.  One of them is a South Dakotan about my age, Kip Sorlie:

“My life requires purpose, something more important than myself.  With my children gone, I found purpose once again in cowboy verse.  It is an honest, straight-forward handshake with honest, straight-forward people who, even if they do not live the life style, carry the values with great pride.  It is for them that I hope to be, at least partially, successful.”

Here’s a humble man who doesn’t carry on and swagger.  We need fewer cowboys in the White House and more of them doing what they do best, wrangling and writing poetry.

I swear this tale is true!
   But I've embellished it,
As storytellers do
   To make the pieces fit!

Of men who lived this tale,
   Two have long departed.
The third awaits a trail,
   The fourth has not started.

A son may sometimes spurn
   A dad, too proud to hope.
But in the end they learn
   From withered, weathered rope.

The first rope wagoned in
   Was fated on to me.
It's tied to where I 've been
   And where I hope to be.

-- Epilogue to "Rope" by Kip Sorlie, from "Cowboys Are The Magic"
   Hardcover volume is available for $30 postpaid from:
   Kip Sorlie, 24327 446th Ave., Winfred, SD 57076

Happy Thanksgiving to all my virtual pardners.  See you on the trail — Charley

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