Coin Weighing Puzzle

 Here's a favorite coin-weighing puzzle.

There are six bags of coins. Within each bag, all coins are identical.  Some bags have gold-plated coins that each weigh 5 grams.  The other bags have solid gold coins that each weigh 6 grams.  You have a scale that measures precisely and accurately to the nearest 1 gram.  You may remove coins from any or all bags and weigh them, but you are allowed only ONE weighing after which you must identify which bags have gold coins and which bags have plated coins. 

Try to come up with a solution before reading mine.

Solution:  Label the bags 1 through 6.  Remove 32 coins from bag No. 1, 16 coins from bag No. 2, 8 coins from bag 3, 4 coins from bag 4, 2 coins from bag 5 and 1 coin from bag 6.  Put all the coins together onto the scale and record the total weight, W, in grams.  Determine R=W-315.   Express R in binary notation. For example, if W=368 g. then R=368-315=53 grams.   In binary form, 53= 1 1 0 1 0 1.  The six binary digits correspond to the six bags in that order, i.e., Bag 1 = 1, Bag 2 =1, Bag 3 =0, Bag 4 =1, Bag 5 =0 and Bag 6 =1.  Bags with a "1" have solid gold coins and bags with a "0" have gold plated coins.

 

Loose Change

So I was wondering about the distribution of coins in loose change.  If most of loose change is a result of transactions where you get change for a random purchase that you have paid for with bills, how many of each coin are you likely to have?  First, assume the amounts of the random purchases are uniformly distributed between one cent and 99 cents more than an even number of dollars.  Then what I did was determine how you would receive change in quarters, dimes, nickels and pennies, assuming the change was delivered in the most efficient way, i.e., minimum coins.   For example, if the purchase was $4.31,  and you presented a $5 bill, you would receive your 69 cents as two quarters, one dime, one nickel and four pennies. I examined every possible amount of change from even dollars and totaled the number of each coin.  The result was 150 quarters, 80 dimes, 40 nickels and 200 pennies.  This reduces to 15 quarters, 8 dimes, 4 nickels and 20 pennies for a total value of $4.95.  So these ratios should apply to any random collection of loose change.

Next I wanted to know the value of this change in dollars per pound.  The weights of modern coins are quarter = 5.67 g., dime = 2.268 g., nickel = 5.0 g. and penny = 2.50 g.  This means the weight of the $4.95 group is  173.2 g. or 0.3815 pounds and this gives the value of loose change as $12.98 per pound.  So if you have a container of change that weighs 20 pounds, it probably contains about $260.

So if you throw your loose change into a jar or drawer, check it and you should find you have fewer nickels than any other coin and more quarters and pennies than any others.  I have left half-dollars out of this analysis because they are so rarely seen.

The Other Side of GAS

There has been some chatter on the PhotoClub mail list about Gear Acquisition Syndrome (GAS).  My comments have been that you should be out taking pictures instead of lusting over the latest hardware.  (TMP as an antidote for GAS).   This blog entry is a defense of hardware acquisition.  There is a concurrent thread on the Leica Users Group (LUG) titled "What do you do with last year's camera?".   Posters have weighed in with their plans for keeping or disposing of older model cameras.  Even Leica owners upgrade from time to time.

All of the above got me thinking about why someone holds onto old cameras while buying new ones.  I think there are more reasons to have and enjoy a camera than just using it to make images.  There is the same sort of pleasure one gets from having a nice car, or golf clubs or firearms or woodworking tools.  I call it "tool pleasure".  It is the satisfaction of holding and operating a precision instrument.  Noticing the craftsmanship, fit and finish.  Dryfiring a handgun is only a step down from actually firing the weapon. 

If you have a camera that is well-designed, that feels comfortable in the hand and in which the controls operate smoothly and positively, you get pleasure from owning it and handling it.  Even looking at it.  You may want to put it on a shelf where you can see it often even if you never take pictures with it.  And the only acceptable excuse for selling it is to get funds to acquire a newer model. 

Photographic Stories

There are two types of photographic stories.  First is the photographer's story about the photo image.  How and why was it made?  What gear and what settings?  Where was it made and when?  Then there is the story the photograph tells to the viewer.  If you listen with your eyes and your imagination, the photograph will tell you a story.  What questions does it invoke?  What emotions does it arouse in you?  I will  illustrate these stories with two examples from my own experience.


Unaware

Photographer's Story:  A few years ago I took my wife downtown to get excused from jury duty.  She had compelling medical reasons why she couldn't endure sitting on a jury, but had to go to the assembly to get excused.  It was a chilly day and I chose to wander around the Main Plaza area with my camera to see if there were any good photo subjects.  I saw this young man against the San Fernando Cathedral wall shielding himself from the wind and decided to photograph him when someone walked by.  These two walkers were on their way to the courthouse and I snapped them as they walked by.  Neither the walkers nor the young guy paid any attention to the other, so I titled this "Unaware".

The Photograph's Story:  We do not know the story of either the young man or the walkers, but can imagine that even though they do not acknowledge each other's existence, their paths may cross some day in the future.  Imagine that the young man may someday be falsely accused of a crime.  Maybe he will commit a crime.  The walkers, who may be lawyers, may try his  case.  Maybe  one of them will be the prosecutor and the other hired to defend him.  They will have no idea that their paths crossed years earlier and this  image captured that passing.

Been there, Done  that

Photographer's Story:

I was  killing time at North Star Mall.  In a concourse  between Victoria's Secret Store and other  stores there was a coffee kiosk.  I got a cup of coffee and settled at a small table.  On an extra chair, I positioned my camera so it  was pointed at a Victoria's Secret advertising window.  My Lumix cameras have fully articulated LCD's so I as able to aim the camera and watch the LCD without anyone noticing.  I had a shutter release in my hand, so I could sip my coffee and snap shots whenever I wanted.   I took a few dozen exposures of which I later decided I had maybe three or four keepers.  This is one of them.

The Photograph's Story:

I imagine the lady shown in silhouette to be middle aged, maybe 25 years older than the model in the advert.  She is going about her business, doing some mall shopping.  Maybe 25 years ago she was a hot party girl.  Now she has other priorities of career and family.  When she passes the window, she may notice the advertisement in her peripheral vision, but does not slow down or turn to look.  She realizes that was then and this is now.  Hence, "Been there, done that".   



THE EARL OF TV

In 1968, give or take a year or two, I was working in Houston at AMF Tuboscope, a pipe inspection company, developing new technology for inspecting oil field pipe and pipelines.  We had a sister company in Canada, North American Inspection, that specialized in field inspection of transmission pipelines.  In particular, they were radiographers who examined the pipe welds between joints of pipe before the pipe was buried in the ground.  To add to their capability, we took on a project to develop an internal crawler robot that would carry a radioactive source along inside the pipe and deploy it at each girth weld where film had been wrapped around the outside of the weld.  Upon development of the film, the weld quality could be determined and cracks, porosity and other defects identified.  I was project engineer of this project and did the electronic design for the control system.

The crawler was a self-contained, autonomous device powered by an on-board 24 volt battery.  It was driven by a high-torque DC motor connected to a drive wheel.  The control system, consisting of discrete analog and digital IC’s was contained in an aluminum housing about 8-inches on a side.  Control knobs and switches on the top of the housing permitted set-up of the device.  The radioactive source was a cobalt isotope housed in a 200-lb. holder of spent uranium or lead.  When the robot sensed a weld, it stopped and a separate drive motor would drive the isotope from its holder into position to expose the film for a preset exposure time then it would be retracted back into a safe position and the crawler would move to the next weld.

The system was built and checked out in our Houston lab, then taken to a field site in Louisiana where it was used with North American radiographers for training before it was shipped to Canada.  All went well and the system was turned over to the North American company office in Calgary.  Not unexpectedly, we got a call within the next few weeks that there were problems with the control system.  I bagged up some spare parts, a few tools and a couple of test instruments and headed to Calgary.  As I went through customs, the Canadian authorities were interested in my little Sony battery powered oscilloscope and my function generator.  I explained the situation, but they said I could use Canadian instruments and confiscated my gear.  I pled my case to my North American contact, the office manager there, and he said he would see what he could do.  I told him I need some electronic workbench space to trouble shoot the system.

He came back later in the day and said, “I’ve found you a place to work.  It is the repair shop at a TV store.  The Earl of TV would close at 9 PM and I could use his shop all night long.”  OK, maybe this won’t be too bad.  I showed up at The Earl of TV and sure enough he had a work bench.   I had the electronics box from the robot and got ready to do my trouble shooting.  First problem:  The electronics required 24 VDC and the shop had only a 12 volt supply.  I dug around through everything in the shop, but no luck.  He did have some pliers, though, and fifteen minutes later, the 12 volt supply, in series with the battery from my rent car gave me the 24 volts I needed.  I thought surely there must be an audio oscillator or some such generator to produce an AC test signal.  Sorry, no oscillator, but I  did find, in his junk drawer, a filament transformer that let me produce at least a 60 Hz sine wave of a low voltage.  His oscilloscope, I will never forget it, was a Jackson CRO-2.  It did have a display, but no DC coupling.  If you connected the probe to a DC potential, the trace would sail off the screen and slowly drift back as the input capacitor charged up.  I won’t go into the agony of trouble-shooting digital switching circuits with an AC scope, but it was not fun.  To cut to the chase, I did survive the night and got the box working in time to turn it over to the North American crew the next day.  

One final touch:  On the day I was to return to Houston, I decided to pay a courtesy call to the Tuboscope Calgary office.  They were doing oil field inspections completely independent of the North American Inspection Company.  When I drove into the yard at the Tuboscope location, I saw a neat looking van painted in the company colors.  It had a Texas license plate.  I said, “Is someone here from the home office?”  Oh yeah, that’s the Quality Control van.  They are here to check our equipment.  The van had racks of power supplies, scopes, signal sources, etc.   If only I had known.  But then I’d never got to meet the Earl of TV.  Over 20 years later, on another trip to Calgary, I checked a phone book and sure enough The Earl was still listed.  I really doubt that he ever repaired a TV, though.

The Eyes Have It

Here is one of my photos at the India Festival.

I enlarged her left eye and one can see reflections of me and two other customers. I am the one in the dark blue shirt and blue jeans.

They say the eye is the window to the soul.  It is also a mirror to the observer.

Photos of Phaces

The Viewfinder Challenge for March is "Human Faces".  Since I have no local family to photograph (Elaine is camera-shy), I decided to try for faces of strangers.  There was a India Festival at La Villita yesterday so I went there looking for subjects. I had hopes there would be Sikhs in attendance as the ones in turbans and heavy beards make good photo subjects.  None were there while I was there.  I asked a jewelry vendor and a fashion coordinator to take their pictures and they said OK.  The man actually insisted that I take his photo and asked about my Lumix camera.  On the way from La Villita I saw a musician on a porch so I asked him to take his photo and he said OK also.  Photos follow.