Is this cool with you?

bobbym · 2011-03-14 15:18:29

Hi gAr;

The problem really only makes sense when we think of it with A and B being absorbing.

bobbym · 2011-03-16 02:29:47

New problem!

f(n) is defined for all positive integers and f(1) is 1996. If

for all n>1. Find f(5000).

A says) Recurrences are my thing. Have you read my book, "Recurring Recurrences," B? If you could understand it.

B says) That is almost right except that 2 digits are switched in your answer.

C says) I have read A's book and I cannot wait for the movie. But here B is right 2 digits are switched.

Can you fix A's answer?

gAr · 2011-03-16 03:07:57

Hi bobbym,

bobbym · 2011-03-16 03:25:29

Hi gAr;

bobbym · 2011-03-16 20:22:05

New problem!

4 envelopes contain coins. The coins consist of pennies, nickels, dimes and quarters. There is at least 2 of each type in each envelope. No two envelopes have the same combination of coins.
All 4 envelopes have the same total amount of money. What is the minimum amount of money in each envelope.

A says) $1.00 even and that is the smallest answer.
B says) There are a couple of answers smaller than that.
C says) Yep, a dollar sounds right.
D says) B is right 89 cents is the answer.

phrontister · 2011-03-16 22:00:37

Hi Bobby,

Had to look up U.S. coin values.

gAr · 2011-03-16 22:31:57

Hi bobbym,

Last edited by gAr (2011-03-16 22:34:10)

bobbym · 2011-03-16 22:55:31

Hi

phrontister · 2011-03-17 01:17:26

I couldn't think of anything formulaic (unlike gAr's nice method...whatever that is and however that works).

Wrote down the obvious starting number and then went for T&E, mainly.

bobbym · 2011-03-17 01:22:12

Hi phrontister;

I understand how you solve problems and I am fine with that. gAr used a generating function. They are very useful for counting problems. I could teach you them whenever you are ready since you have access to a CAS.

phrontister · 2011-03-17 01:40:52

Thanks, Bobby...I might take you up on that offer one day. Only 40 years to go to retirement!

bobbym · 2011-03-17 01:47:14

Yes, you are what, 28 or 29? That gives you a lot of time.

I wish you would but I will wait until you are ready. I meant take me up on the offer, not that you should retire.

phrontister · 2011-03-17 02:46:01

bobbym wrote:

Yes, you are what, 28 or 29?

When you solve my Y.O.B. puzzle you'll find out my real age (if you can believe me)...but don't reveal it to Tigeree because last year in the '13' thread she said she loves me because she thinks I'm 1 year younger than she is (that reminds me of the movie "Shallow Hal"). Then some time later she changed my age to 27 for some unknown reason, and I'm running with that one for now.

Last edited by phrontister (2011-03-17 02:59:17)

bobbym · 2011-03-17 03:15:24

Hi phrontister;

My lips are sealed. She will never know from me.

bobbym · 2011-03-19 01:29:38

New problem!

52359 is really a special number. It is the sum of 10 different cubes. Find those cubes.

A says) Question is all wrong! It is the sum of 5 cubes, not 10!
B says) Will you stop blurting out wrong answers please. I have the right answer and it is a prime example of what I have just been working on.
C says) I have the answer!
D says) I guess you missed that big clue A, that B let slip. Two of them in fact.

gAr · 2011-03-19 02:25:03

Hi bobbym,

bobbym · 2011-03-19 02:30:22

You could think of it as a knapsack problem and whether it would be easy without the hints? That depends on how you solved it and which of the two hints you concentrated on.

gAr · 2011-03-19 02:34:13

I calculated the maximum cube possible less than 52359. Then observed the prime numbers less than that.

bobbym · 2011-03-19 02:45:38

Hi gAr;

gAr · 2011-03-19 03:04:00

Hi bobbym,

Thank you!

I tried that too when searching for answer:

Using mpmath:

>>>identify(52359,['8','27','125','343','1331','2197','4913','6859','12167','24389'])
'(1*27 + (-1)*125 + 1*343 + 1*1331 + 1*2197 + 2*4913 + 4*6859 + 7*12167 + 12*24389)/8'

>>> pslq([mpf('52359'),8,27,125,343,1331,2197,4913,6859,12167,24389])
[0, 0, 2, 0, 0, 2, 1, -1, 0, 0, 0]

Then by using arprec-2.2.7:
Relation: 0 =
+ 0.* 52359
+ 0.* 8
+ -2.* 27
+ 0.* 125
+ 0.* 343
+ -2.* 1331
+ -1.* 2197
+ 1.* 4913
+ 0.* 6859
+ 0.* 12167
+ 0.* 24389

Hence for those involving integers I have decided only to program!

Last edited by gAr (2011-03-19 03:05:18)

bobbym · 2011-03-19 03:14:46

Hi gAr;

I see what you mean. If I have a complaint about mpmath it is that they are using the Ferguson algorithm. The later LLL is much faster and more robust.
I remember that I could not even get the algorithm they mention to work.

Pari or Maxima might have a PSLQ also. I understand that Sage can run other packages through its interface.

gAr · 2011-03-19 03:33:58

Hi bobbym,

I tried PARI. It allows us to choose from the algorithms. But none gave the vector [1,1,...1].
I don't know if it's implemented in maxima.

bobbym · 2011-03-19 03:39:16

Hi gAr;

Okay, no problem. You got the right answer. Thanks for working on the problem.

gAr · 2011-03-19 03:47:44

Not a problem, I got to know about those algorithms.
Thank you!

bobbym · 2011-03-21 13:42:19

Hi gAr;

Your welcome:

New problem!

How many arrangements are there of n,n,n,n,m,m,m,o,o,o with no adjacent letters being the same? No computers allowed please.

A says) Well that stops you B, you can not buckle your shoes without doing a million iterations on your blasted machines. I did it by PIE and got 3769.

B says) Sorry A but that is wrong, I have the right answer and I did not use a computer.

C says) I have it! It is 284.

D says) It is 300, and I love the movie.

B says) Nope! I am the only one to solve this in existence. C, your answer has 2 digits switched then it would be right!

A says) B is cracking up. First he thinks he is the only problem solver in existence and he has the wrong answer too. C has no correct digits.

Math Is Fun Forum

#326 2011-03-14 15:18:29

Re: Is this cool with you?

#327 2011-03-16 02:29:47

Re: Is this cool with you?

#328 2011-03-16 03:07:57

Re: Is this cool with you?

#329 2011-03-16 03:25:29

Re: Is this cool with you?

#330 2011-03-16 20:22:05

Re: Is this cool with you?

#331 2011-03-16 22:00:37

Re: Is this cool with you?

#332 2011-03-16 22:31:57

Re: Is this cool with you?

#333 2011-03-16 22:55:31

Re: Is this cool with you?

#334 2011-03-17 01:17:26

Re: Is this cool with you?

#335 2011-03-17 01:22:12

Re: Is this cool with you?

#336 2011-03-17 01:40:52

Re: Is this cool with you?

#337 2011-03-17 01:47:14

Re: Is this cool with you?

#338 2011-03-17 02:46:01

Re: Is this cool with you?

#339 2011-03-17 03:15:24

Re: Is this cool with you?

#340 2011-03-19 01:29:38

Re: Is this cool with you?

#341 2011-03-19 02:25:03

Re: Is this cool with you?

#342 2011-03-19 02:30:22

Re: Is this cool with you?

#343 2011-03-19 02:34:13

Re: Is this cool with you?

#344 2011-03-19 02:45:38

Re: Is this cool with you?

#345 2011-03-19 03:04:00

Re: Is this cool with you?

#346 2011-03-19 03:14:46

Re: Is this cool with you?

#347 2011-03-19 03:33:58

Re: Is this cool with you?

#348 2011-03-19 03:39:16

Re: Is this cool with you?

#349 2011-03-19 03:47:44

Re: Is this cool with you?

#350 2011-03-21 13:42:19

Re: Is this cool with you?

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