What's new
By:
USCHO Fan Forum

This is a sample guest message. Register a free account today to become a member! Once signed in, you'll be able to participate on this site by adding your own topics and posts, as well as connect with other members through your own private inbox!

  • The USCHO Fan Forum has migrated to a new plaform, xenForo. Most of the function of the forum should work in familiar ways. Please note that you can switch between light and dark modes by clicking on the gear icon in the upper right of the main menu bar. We are hoping that this new platform will prove to be faster and more reliable. Please feel free to explore its features.

Monty Hall, we have a PROBLEM

Re: Monty Hall, we have a PROBLEM

Brenthoven said:
I love playing the "change game." It confuses so many people who can't do math.

And many LED signs/etc DON'T show that extra .009 cents. I'm 99% sure Holiday Gas Stations don't show it. I don't recall on the pumps, though.
Click to expand...
Its a Seals, Weights and Measures thing, you don't show it, I wouldn't pay it and neither would many folks. You have a whole Dept in your state gov't watching gas pumps, scales and the way goods are sold by weight, volume etc Most gas stations if going up in price will change sign before changing pump prices, so customers don't b itch. Going down in price, change pumps and then change sign.
 
Re: Monty Hall, we have a PROBLEM

LynahFan said:
But you'd also need to know the average number of items per transaction - even if everything is 99 cents with 6% sales tax ($1.05 per item), you might think you would get lots of quarters. But if the typical order is 36 items, that's $37.78 and those orders would get no quarters at all.

It also depends how many customers are engineers and would hand over $40.03 for that $37.78 transaction to get $2.25 in return. :D
Click to expand...

The specification of the problem removed your last sentence from consideration. "you always pay using only bills, even if you go to three or four stores in a row."

Now, in real life, when I have them, I generally tend to give enough pennies / nickels / dimes when I pay so that I only get quarters in return. I then save up the quarters and give them to the kids when they come home so that they can then use them do to laundry when they go back to their apartments.


Before doing any math, I'd intuitively expect to get pennies, quarters, dimes, and nickels in descending order, and I'd expect to get about twice as many dimes as nickels.

To do math, we'd need to make some simplifying assumptions, which might or might not actually be true in real life.

The first simplifying assumption, which is definitely not true in real life (!), is that you get the "most efficient" change: $0.35 is a quarter and a dime, not three dimes and a nickel (which I've received a few times), or $0.56 is two quarters, a nickel and a penny, and not five dimes, a nickel, and a penny (hmm...maybe some clerks are just confused by quarters and only use dimes and nickels??).

The other assumption is that your distribution of change is fairly random. You are roughly as likely to get anything from no coins to nine coins as change depending upon the sale amount (though one could alter this assumption and say everything is priced at $xx.x9, but then you have to make assumptions about how many items you buy and what your state / local sales tax rate is).

Given these two assumptions, then you get rough proportions as follows: two dimes for each nickel, five pennies for each nickel, and three quarters for every four pennies (or on average, each time you receive change, 2 pennies, 1.5 quarters, 0.8 dimes, and 0.4 nickels). Adjusting for "real life" you'd get even fewer nickels, more dimes, and fewer quarters, but probably not enough to change the relative order.
 
Last edited:
FreshFish said:
The specification of the problem removed your last sentence from consideration. "you always pay using only bills, even if you go to three or four stores in a row."

Now, in real life, when I have them, I generally tend to give enough pennies / nickels / dimes when I pay so that I only get quarters in return. I then save up the quarters and give them to the kids when they come home so that they can then use them do to laundry when they go back to their apartments.


Before doing any math, I'd intuitively expect to get pennies, quarters, dimes, and nickels in descending order, and I'd expect to get about twice as many times as nickels.

To do math, we'd need to make some simplifying assumptions, which might or might not actually be true in real life.

The first simplifying assumption, which is definitely not true in real life (!), is that you get the "most efficient" change: $0.35 is a quarter and a dime, not three dimes and a nickel (which I've received a few times), or $0.56 is two quarters, a nickel and a penny, and not five dimes, a nickel, and a penny (hmm...maybe some clerks are just confused by quarters and only use dimes and nickels??).

The other assumption is that your distribution of change is fairly random. You are roughly as likely to get anything from no coins to nine coins as change depending upon the sale amount (though one could alter this assumption and say everything is priced at $xx.x9, but then you have to make assumptions about how many items you buy and what your state / local sales tax rate is).

Given these two assumptions, then you get rough proportions as follows: two dimes for each nickel, five pennies for each nickel, and three quarters for every four pennies (or on average, each time you receive change, 2 pennies, 1.5 quarters, 0.8 dimes, and 0.4 nickels). Adjusting for "real life" you'd get even fewer nickels, more dimes, and fewer quarters, but probably not enough to change the relative order.
Click to expand...

tl;dr version: I was right.
 
Re: Monty Hall, we have a PROBLEM

I'm going with the "most efficient combination" of coins returned, although it does make the problem a little less interesting.

20 pennies for every 15 quarters for every 8 dimes for every 4 nickels.
 
owslachief said:
I'm going with the "most efficient combination" of coins returned, although it does make the problem a little less interesting.

20 pennies for every 15 quarters for every 8 dimes for every 4 nickels.
Click to expand...
That can't be quite right - there are 99 possibilities, so it doesn't seem like the ratios should work out quite so evenly. Shouldn't be to hard to check all 99, but my flight is about to depart - exercise left to the reader.
 
LynahFan said:
That can't be quite right - there are 99 possibilities, so it doesn't seem like the ratios should work out quite so evenly. Shouldn't be to hard to check all 99, but my flight is about to depart - exercise left to the reader.
Click to expand...

There's 100 possibilities including 0. But assuming you get the most efficient change back, his numbers are right. You'll average 2 pennies, 1.5 quarters, .8 dimes, and .4 nickels back per transaction. Multiply by 10 to get whole numbers and your long-term average ratio will be 20:15:8:4.

Check my post way down below to show the math for dimes and nickels.
 
Re: Monty Hall, we have a PROBLEM

Answer:
$0.01.....$0.05.....$0.10.....$0.25
2.000.....0.500.....0.800.....1.500

Sales tax (generally) doesn't make a difference. This assumes the price is random.

So yes, the above answers were correct.
 
Last edited:
Re: Monty Hall, we have a PROBLEM

Nix that, sales tax has a minor affect depending on the rate (obviously) and whether you truncate or round.
 
Re: Monty Hall, we have a PROBLEM

physics geeks will love this one, so will engineers....

You are tasked to move a relatively tall / narrow (e.g. 6.5' x 3' x 1.5') somewhat heavy object, and you have a partner with you.

The problem with lifting it from the bottom is that it is hard to control the sway at the top.

But you can't lift it from the middle because of the way it is constructed. The base is about 1/5 of the total height and the remainder is resting atop the base.

The solution to this problem, of all things, was a product I'd bought from one of those TV ads: the "forearm forklift."

Well, here's a testimonial for you. They were fantastic. Very simple concept: furniture straps with openings along the end. You and partner get on opposite sides, slip two straps lengthwise under obect. Each of you then slides opening at appropriate height over wrist down to forearm just above elbow. grab object higher up, straighten arm while your partner dies the same, and the act of straightening the arms also provides the lift you need to get the object off the floor. and you are holding it at its middle and have total control over any sway. it was really awesome to have a product work as well in real life as it was advertised. :)
 
Re: Monty Hall, we have a PROBLEM

FreshFish said:
A much more useful measure than "miles per gallon" is "gallons per 100 miles." Then you can directly compare how much gasoline a car would use when you think about how far you drive, and you could more easily quantify how much it would cost you to fuel it.
Click to expand...

I spend my time in traffic watching my MPG readout and doing that conversion in my head. A couple weeks ago on the Leesburg bypass (a place you do not want to be during rush hour on Friday) my MPG dropped below 2.0 over a short stretch, which equates to 50 gallons per 100 miles. I don't think Russian tanks even get that bad mileage.
 
Re: Monty Hall, we have a PROBLEM

This is a pretty old one and was a lot more challenging before internet search engines became so robust.

Name the colleges/universities that can count among their graduates both a President of the United States, and a Super Bowl winning quarterback.

Bonus: name the Presidents and quarterbacks.


PS if anyone wants a hint or two, LMK and I can post it in white text.
 
Re: Monty Hall, we have a PROBLEM

FreshFish said:
This is a pretty old one and was a lot more challenging before internet search engines became so robust.

Name the colleges/universities that can count among their graduates both a President of the United States, and a Super Bowl winning quarterback.

Bonus: name the Presidents and quarterbacks.


PS if anyone wants a hint or two, LMK and I can post it in white text.
Click to expand...

(an answer whited out below)

The Maize and Blue Weasels, Gerald Ford and Tom Brady.
 
You must log in or register to reply here.
Back
Top