Note to self

[lewelma]

Over the years, my older boy has been known to leave a note to himself about something he needs to remember to tell me, something that he is thinking about while laying in bed at night. He leaves it in front of his bedroom door so he will see it coming out or I will see it coming in.  They used to be quite cute with misspelled words or crazy sloppy handwriting.  It might say something like 'make a birthday present for xxx', or 'don't wake me up early as I had a late night'.  So this morning, I find a little note and pick it up.  It's been at least 6 months since the last one, and I am curious to see what it says. Well, I guess my boy is growing up; it said:

 

Chinese Remainder Theorem

Light bulb logic problem from the Art and Craft of Problem Solving.

 

Hummm,  don't think this one was for me. :001_smile:

[mliss]

I write "Note to Self" sticky notes but they are all boring like "take out the trash" or "remember to call so-and-so."  I have no idea what Chinese Remainder Theorem is  :huh:   

[kiana]

I write "Note to Self" sticky notes but they are all boring like "take out the trash" or "remember to call so-and-so."  I have no idea what Chinese Remainder Theorem is  :huh:   

 

Number theory :D

 

In its basic form, it is used to solve problems like this:

 

An old woman goes to market and a horse steps on her basket and crashes the eggs. The rider offers to pay for the damages and asks her how many eggs she had brought. She does not remember the exact number, but when she had taken them out two at a time, there was one egg left. The same happened when she picked them out three, four, five, and six at a time, but when she took them seven at a time they came out even. What is the smallest number of eggs she could have had?

 

(posed in a text by Brahmagupta, 7th century AD)

[musicianmom]

I don't know how to work the problem, but I got far enough to figure out that's a lot of eggs for one basket!

[quark]

Number theory :D

 

In its basic form, it is used to solve problems like this:

 

An old woman goes to market and a horse steps on her basket and crashes the eggs. The rider offers to pay for the damages and asks her how many eggs she had brought. She does not remember the exact number, but when she had taken them out two at a time, there was one egg left. The same happened when she picked them out three, four, five, and six at a time, but when she took them seven at a time they came out even. What is the smallest number of eggs she could have had?

 

(posed in a text by Brahmagupta, 7th century AD)

 

Thank you! This problem sounds like an easier explanation than kiddo's explanation about mod something or other. I listened politely as he explained it then went to clear my garage, after which I felt less stupid and unproductive. :lol:

 

[kiana]

Thank you! This sounds like an easier explanation than kiddo's explanation about mod something or other. I listened politely as he explained it then went to clear my garage, after which I felt less stupid and unproductive. :lol:

 

 

Well ... my mother listened politely and said "that's nice, dear" when I tried to explain my dissertation to her. It doesn't get better :p

[Alte Veste Academy]

Number theory :D

 

In its basic form, it is used to solve problems like this:

 

An old woman goes to market and a horse steps on her basket and crashes the eggs. The rider offers to pay for the damages and asks her how many eggs she had brought. She does not remember the exact number, but when she had taken them out two at a time, there was one egg left. The same happened when she picked them out three, four, five, and six at a time, but when she took them seven at a time they came out even. What is the smallest number of eggs she could have had?

 

(posed in a text by Brahmagupta, 7th century AD)

No fair to post a cliffhanger!

[kiana]

No fair to post a cliffhanger!

 

The lazy way to solve this problem is:

 

Let n be the number of eggs so I don't have to write "the number of eggs" over and over again.

 

n must be one more than a number which is a multiple of 2, 3, 4, 5, 6. The least common multiple of 2, 3, 4, 5, 6 is 60. So n must be one more than a multiple of 60. n also must be divisible by 7. Let's just list off numbers that are one more than a multiple of 60 until we get to one that's divisible by 7. 61, 121, 181, 241, 301 ... ta-da! And yes, that's a boatload of eggs. Maybe they were quail eggs.

 

However, this solution used trial and error, which is fine for numbers of this magnitude, but sub-optimal with larger numbers. Explaining the Chinese Remainder theorem and using it to solve this problem would require explaining modular arithmetic and a fair amount of background. However, once you HAVE the theorem, you can use it to solve arbitrary problems like this much more quickly.

[Alte Veste Academy]

The lazy way to solve this problem is:

 

Let n be the number of eggs so I don't have to write "the number of eggs" over and over again.

 

n must be one more than a number which is a multiple of 2, 3, 4, 5, 6. The least common multiple of 2, 3, 4, 5, 6 is 60. So n must be one more than a multiple of 60. n also must be divisible by 7. Let's just list off numbers that are one more than a multiple of 60 until we get to one that's divisible by 7. 61, 121, 181, 241, 301 ... ta-da! And yes, that's a boatload of eggs. Maybe they were quail eggs.

 

However, this solution used trial and error, which is fine for numbers of this magnitude, but sub-optimal with larger numbers. Explaining the Chinese Remainder theorem and using it to solve this problem would require explaining modular arithmetic and a fair amount of background. However, once you HAVE the theorem, you can use it to solve arbitrary problems like this much more quickly.

Thanks! I am a big fan of lazy! :tongue_smilie:

[lewelma]

Thanks for explaining it!  I just kind of went :confused: :huh: and a bunch of :D .  I hope I have kept some of his notes from when he was younger, sure would be fun to display the development of his notes at his 21st b-day party.