General Mathematics

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Tdarcos
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Re: General Mathematics

Post by Tdarcos »

raecoffey wrote: Tue Feb 07, 2023 6:50 pm
Tdarcos wrote: Tue Feb 07, 2023 11:40 am There are other math systems that use intrinsic properties of numbers to make calculations easier than the standard single multiply and shift mode for multiplying two numbers. One I happen to like is the Trachtenberg System. There are others.
Can you name some others?
Chisanbop was one I remember there was a book being sold on TV to teach kids an easier method of arithmetic.
raecoffey wrote: Tue Feb 07, 2023 6:50 pm Why do you like that system?
Because it [Trachtenberg System] was the first one I ever discovered after finding the 1960 book by Ann Cutler. Wikipedia gives a partial description of the system.

Now, realize that mathematics were mostly developed by Arab scholars during the dark ages. Consider this: how is multiplication done? From right-to-left, the way Arabic is written. Trachtenberg developed his system while in a Nazi Concentration Camp as a way to keep his sanity; the system relies on using as little paper as possible because it was very hard for Trachtenberg to obtain. Some calculations are done right-to-left, others left-to-right depending on which is easier.

One example is how to multiply by 2; you would normally do it right-to-left, so 316802 x 2 is computed as 2x2=4, 0, 2x8=(carry 1)6, 2x6+1=(carry 1)3, 1x2+1=3,2x3=6, or 633604. But using Trachtenberg's system it's done left-to-right using 1 rule:double each digit (with carry) so you can compute double almost as fast as you can write it 483267 x 2 is 8 16 (so add 1 to first digit making it 96) 6 then 4, 12, so make that 52, 14, making it 534 for result of 966534.

Now, let's do 6% sales tax. The rule for multiply by 6 is:
* From right, add half of the neighbor (digit to right) to each digit. If the current digit is odd, add 5.

$710.43 - 3 has no neighbor, add 5 =8
4 + 1 (1/2 of 3) =5
0 +2 (1/2 of 4) =2
1+5+0 =6
7+5+0(1/2 of 1)=12, write 2, carry 1
0 (digit to left of 7)+3+1(carry)=4
426258 or $42.63
raecoffey wrote: Tue Feb 07, 2023 6:50 pm What is your definition of intrinsic here dealing with math?
E.g. in this system, the intrinsic for multiplying by 6 is you add each digit plus 1/2 of digit to right plus 5 if this digit is odd. There are specific rules to make each number calculation. A separate set of rules for large numbers, for division, and others.
raecoffey wrote: Tue Feb 07, 2023 6:50 pm And can you please give me an example of one of these " intrinsic propetries" in motion, mathematically? I don't understand how anyone can try to talk about science, especially mathematics using only words.
I am a computer programmer. Algorithms - the method of describing how to solve a problem - will be done with the mathematical notations of the language used to write the code used to perform the function. But the general method of how it is done is generally described in English.
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Re: General Mathematics

Post by Jizaboz »

raecoffey wrote: Tue Feb 07, 2023 6:50 pm
Tdarcos wrote: Tue Feb 07, 2023 11:40 am There are other math systems that use intrinsic properties of numbers to make calculations easier than the standard single multiply and shift mode for multiplying two numbers. One I happen to like is the Trachtenberg System. There are others.
Can you name some others? Why do you like that system? What is your definition of intrinsic here dealing with math? And can you please give me an example of one of these " intrinsic propetries" in motion, mathematically? I don't understand how anyone can try to talk about science, especially mathematics using only words.
Tdarcos wrote: Wed Feb 08, 2023 1:26 am I am a computer programmer. Algorithms - the method of describing how to solve a problem - will be done with the mathematical notations of the language used to write the code used to perform the function. But the general method of how it is done is generally described in English.
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Re: General Mathematics

Post by raecoffey »

... still waiting...

Or... question change?

Dint let tge math thread die!
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Re: General Mathematics

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Here is a puzzle.

You have a 6' ruler, a stopwatch, 300' of rope, a portable digital barometer, and if necessary, the help of the building superintendent, and your objective is to determine the exact height of the building, which is about 35 floors. The super will not help with the work, but will unlock any doors needed (or loan you the key) or supply necessary information, like where the roof access door is.

Name all the different ways you can find out what the building's height is.
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Re: General Mathematics

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Problem #2 (And try doing this without using the internet).

Two kids from a family are talking.

The Girl: This is unfair! I have twice as many brothers as sisters!
The Boy: That's wrong, sis. We have the same number of brothers and sisters.

1. Both statements are correct.
2. You have enough information to tell us the number of children in that family and their sexes.


I told this to one of my teachers, he solved the problem in a few seconds, and he was my English teacher. This explained why once, in math class, our math teacher told us our most important class was English.
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Problem #3

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Problem #3. Which weighs more, a pound of silver or a pound of feathers?
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Problem #4

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You have a clothes line with 12 birds sitting on it. You usea slingshot and a rock to hit one of them and knock it off. How many remain?
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Problem #5

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How many times a day, and which times of day look exactly the same on an analog clock with no digit numbers when seen directly or in a mirror?

Depending on how you want to look at it, there are two possible answers.
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Problem #6

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A man tells his his daughter to be home from her date by midnight. She and her boyfriend can't get back until 2:30. Everyone is asleep, so she realizes she has to be able to tell hi when she got in without lying. She tells him to wait, then at 2:59 she gets out, tells him what to say if he's questioned. She goes in at precisely 3am, goes up to bed, gets in and goes to sleep.

Next morning, her father asks her when she got back. She tells him that she got back in at exactly a certain time. He is (internally) relieved she did not come back really late, like 2 or 3 AM. What she said, on its face, was not a lie. What time did she say she got in at?
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Re: General Mathematics

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Oh now it's Puzzle Corner!

yay

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Problem #7 & #8

Post by Tdarcos »

Problem #7
You are the logistics manager for a communications relay service in outer space. A critical beacon orbiting an artificial satellite was destroyed by a spaceship crashing into it. (The beacon reported its telemetry and radar data including approaching vehicles - that's part of its job - until the signal stopped.) A technician has to go install a new beacon. The satellite is 250 sectors away, a resupply ship can carry enough food and living supplies (water, air, air filters, etc.) for 5 person-days and enough fuel for 60 sectors. (These ships are usually for short trips. The long-distance ship is so far away it would take a year to get back as it's in another direction.)A ship with no crew could carry enough fuel for 70 sectors; food and fuel are interchangeable such that each person-day of food takes 2 sectors of distance- and each 2 sectors of fuel reduces crew survival time 1 person-day.

A ship's speed is 10 sectors/day. The ship carrying the beacon has only enough storage for 5 person-days and 50 sectors; once it drops the beacon, it would then have fuel capacity to travel 60 sectors. Replacing and starting the beacon plus testing require 1 day.

Resupply ships can be returned to home base unattended (it can follow the home base beacon), if they have enough fuel to return but cannot be piloted to the satellite without at least one attended control ship with a pilot (no beacon to lock onto). Fuel is presumed used on a 1/2 start, 1/2 stop basis; 1/2 of the fuel is used to accelerate the ship fast enough to travel 30 sectors at 10 per day, then 1/2 the fuel is needed to decelerate (brake) the ship. Ships connected together can transfer fuel between each other automatically and flip between accelerate and brake by computer.

What is the minimum number of ships necessary to be sent out to replace the beacon and return the technician (and all resupply operators) alive and unhurt to home base?

You may want to write a program or use a spreadsheet to solve this.

Show the solution.

Problem #8
Same as #7 but every ship requires a pilot to come back.

- - - -
I'm going to be busy writing a program to solve #7, #8, or both. Or discover it's insoluble.
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Re: General Mathematics

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A clarification.
Two or more ships can be bonded together and only require one pilot but all require full fuel to move or brake.
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Re: General Mathematics

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Can a Star Trek transporter be used instead of all the stuff mentioned ?

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Re: General Mathematics

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AArdvark wrote: Sat Feb 11, 2023 6:09 pm Can a Star Trek transporter be used instead of all the stuff mentioned ?
No, this is an update of the "truck rescue" problem which I'll do as #9.
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Problem #9 - Depot Refuel

Post by Tdarcos »

This is the original problem, which I can't demonstrate as Jonsey will not allow me to inline YouTube videos and won't either enable it or tell me why I'n no longer allowed to. So I have to explain it.

You have to deliver fuel to a depot that is empty, 1000 miles away, but your trucks have a 200 mile range. The gasoline delivery trucks run on diesel, diesel delivery vehicle runs on gasoline (yeah, it's so stupid it's probably a government operation). Gasoline delivery trucks have a 20 gallon diesel fuel tank, diesel delivery trucks have a 20 gallon gasoline fuel tank. Both have 200 gallon delivery tanks.

Compute the smallest number of trucks needed to get 1000 gallons of gas and 1000 gallons of gasoline to the depot and get every truck back to the dispatch. If needed, trucks may return on-route and may transfer contents to another tank. All trucks get 10MPG, whether it's a diesel or a gasoline fueled truck.

What is the smallest number of delivery trucks needed and how many of each kind?

Show your work. or show it's insoluble.
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Re: General Mathematics

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Tdarcos wrote: Sat Feb 11, 2023 11:25 am Here is a puzzle.

You have a 6' ruler, a stopwatch, 300' of rope, a portable digital barometer, and if necessary, the help of the building superintendent, and your objective is to determine the exact height of the building, which is about 35 floors. The super will not help with the work, but will unlock any doors needed (or loan you the key) or supply necessary information, like where the roof access door is.

Name all the different ways you can find out what the building's height is.
Head to the roof and ask the superintendent to join you. Start the stopwatch and then push the superintendent over the side. Stop the stopwatch the minute he hits the sidewalk below. With the duration of his fall and the rate of gravity, we can figure the height of the building.

Formula: https://www.vcalc.com/wiki/vCalc/Object ... me+to+drop
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Re: General Mathematics

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Flack wrote: Sun Feb 12, 2023 11:20 amHead to the roof and ask the superintendent to join you. Start the stopwatch and then push the superintendent over the side. Stop the stopwatch the minute he hits the sidewalk below. With the duration of his fall and the rate of gravity, we can figure the height of the building.

Formula: https://www.vcalc.com/wiki/vCalc/Object ... me+to+drop
I like your solution. It shows innovation and creativity. However...

In scenario 1, the superintendent becomes suspicious, grabs you, and both of you are killed before you can get the height. You Fail.
In scenario 2, this takes place in Texas, the superintendent discovers your attempt to murder him, he draws his handgun and kills you. You Fail.
In scenario 3, as soon as the guy hits the ground, emergency services are called, the building is locked down, roof video shows you pushed the super off the roof, unfortunately it was in Louisiana, 5 Louisiana State Police officers show up, holding you down so you can't breathe, and you die before you can give the answer. You Fail.

New Rule: Answers must use methods that do not include crimes of violence. Trespassing, extortion, blackmail, embezzlement and removing the tags of mattresses are permitted. Rape, murder, kidnapping, and killing bald eagles are not permitted.
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Re: General Mathematics

Post by AArdvark »

A fine time to impose parameters to the problem....the Super is already dead and the building has been measured

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Re: General Mathematics

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AArdvark wrote: Sun Feb 12, 2023 5:45 pm A fine time to impose parameters to the problem....the Super is already dead and the building has been measured
No, answers involving criminal violence behavior are disqualified. There are at least a half dozen solutions that do not require the killing or injuring of anyone. So the Super is still alive, and the solution has not been given.
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Re: General Mathematics

Post by raecoffey »

Flack wrote: Sun Feb 12, 2023 11:20 am
Tdarcos wrote: Sat Feb 11, 2023 11:25 am Here is a puzzle.

You have a 6' ruler, a stopwatch, 300' of rope, a portable digital barometer, and if necessary, the help of the building superintendent, and your objective is to determine the exact height of the building, which is about 35 floors. The super will not help with the work, but will unlock any doors needed (or loan you the key) or supply necessary information, like where the roof access door is.

Name all the different ways you can find out what the building's height is.
Head to the roof and ask the superintendent to join you. Start the stopwatch and then push the superintendent over the side. Stop the stopwatch the minute he hits the sidewalk below. With the duration of his fall and the rate of gravity, we can figure the height of the building.

Formula: https://www.vcalc.com/wiki/vCalc/Object ... me+to+drop
Exactly. I remember that boring ass problem, I didn't even want to respond but I liked your superintendent solution.
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