What do you think?

phrontister · 2010-06-09 05:04:27

Hi Bobby,

Yes, that is fast. I like the fact that it lists the permutations, which I haven't been able to do in Excel (I have to enter each permutation manually - but the calculation results are instantaneous).

Why does it include powers of 2? It appears to me that no power or multiple of 2 yields a solution. I don't know the logical argument for excluding 2, though.

I tried to change the code to solve for 3543075, but I must have done something wrong as it only prints about half of the total number of answers (according to LB). I haven't yet understood what your code's doing, so I'm only guessing with my code changes.

Here's what I'm up to. Can you see where I've gone wrong?

FactorInteger[2*3543075]

foo[l_] := Times @@ l;

The next line need adjustment for each new problem;
two = Union[
  foo /@ Permutations[{1, 3, 3^2, 3^3, 5, 5^2, 29, 181}, {4}]]

ans = Solve[{(b + 1) == f, (b + 2 m) == 2*3543075/f}, {b, m}] /. 
  f -> two

Select[MapThread[List, {ans[[1, 2]] // Last, ans[[1, 1]] // Last}], 
 IntegerQ[First[#]] == True && First[#] >= 0 &]

Last edited by phrontister (2010-06-09 11:32:39)

bobbym · 2010-06-09 07:55:45

Hi phrontister;

Just generally saying, you would have to make some adjustments for each new number based on it's unique factorization.

I haven't given the 2's a lot of thought, I wanted to be on the safe side and not miss any solutions.

I can only come up with 48 solutions ( change {4} to 4 in Permutations and put the 2 back between 1 and 3 ) to your new problem. What solutions do you get? I have tried to write the M7 code to mirror the way the problem is solved in the book. It was solved for 1000 a much smaller number. And one with less factors. Also my understanding of the book solution may not be complete. Probably needs some bells and whistles.

phrontister · 2010-06-09 12:06:52

Hi Bobby,

I eliminated 2 because I couldn't get Excel to automatically list all permutations, and typing in permutations including 2 would be tedious and unnecessary. In LB I'd already seen from the dozen or so test cases that included powers or multiples of 2 that 2 was out. No logic to that discovery, though...I can't prove it.

Your changes worked, and I also got 48 solutions in M7. However, it lists 3543075 as a solution...which of course it isn't. LB only lists

Yes...the code may be missing a bell or a whistle.

This is my LB code. Slooooow, but it gets there...and it checks all the options along the way. No doubt it can be improved...probably by using permutations somehow.

    for a = 1 to 1771538
        y = 0
        x = a
        do
        y = y + x
        if y = 3543075 then
            print a
        end if
        x = x + 1
        loop while y < 3543076
    next a
    print "End"
    end

Last edited by phrontister (2010-06-09 12:11:06)

bobbym · 2010-06-09 13:04:47

Hi phrontister;

Change the last line to this:

Select[MapThread[List,{ans[[1,2]]//Last,ans[[1,1]]//Last}],IntegerQ[First[#]]==True && First[#]>=0 && Last[#]!=0&]

That LB code can implemented in 7 too. Just being mindful of syntax of course. The advantage of using 7 is that once you understand the math way, it is easy to just translate it into 7. With all the speed advantages.

phrontister · 2010-06-10 02:32:17

Works fine now thanks Bobby.

...once you understand the math way, it is easy to just translate it into 7.

That would take me a lifetime, given all the spare time I haven't got. Might have to wait until my retirement in 40 years time (at age 67) before I can devote enough energies towards 7 to get a better grip on it. You can help me some more then.

bobbym · 2010-06-10 03:05:50

That would take me a lifetime

It takes everyone a lifetime, some people a little longer. Have you seen the wolfram demonstrations page?

http://demonstrations.wolfram.com/

You can download the scource code and run the ones that interest you. There, you will get an idea of what 7 is capable of.

bobbym · 2010-06-16 21:25:17

Calculate the successive discount of 10%, 20% and 25% on some marked price p.

A says) Can't be done, math doesn't work, just read my paper on cellular mitosis.

B says) Of course math works, you do it like this: I am hiding the solution cause I hate A.

Obi Wan says) Don't give in to hate B, that leads to the dark side.

C says) I don't know I tried your formula on a pair of pants at sears and it didn't work. The pants were too small.

A says) See it's all here, cellular mitosis baby.

D says) That'll work, but isn't there something better?

B says) Sure is!

Can you find B's improved solution?

phrontister · 2010-06-16 22:11:33

Hi Bobby,

I'd do it like this

Re cellular mitosis, I got as far as this in Wikipedia and gave up: "Mitosis is the process by which a eukaryotic cell separates the chromosomes in its cell nucleus into two identical sets in two nuclei."

A's paper on it would have to be many smidgens easier on the eyes than that to hold my interest.

Last edited by phrontister (2010-06-16 22:20:13)

bobbym · 2010-06-16 22:30:15

Hi phrontister;

B's super method is this:

Is that what you have done?

phrontister · 2010-06-16 22:48:54

Yes, that's what I did.

There's a bit of mental arithmetic that got it to that point, but which I didn't show.

bobbym · 2010-06-16 23:07:55

Excellent work then !

Don't worry about A, people like him really squash my zucchini.

Fruityloop · 2010-06-22 12:38:38

Two die are thrown at once. The sample space is 2,3,4,5,6,7,8,9,10,11,12. How many times must this be done on average to get all eleven numbers?

I just got a new computer. But, I wrote a C++ program on my old computer to solve this and I got an answer of about

My compiler dates from 1992! I'm going to have to download a newer one from the Internet.
I can't see an easy way of getting the answer without computer help.

Last edited by Fruityloop (2010-06-22 12:40:09)

bobbym · 2010-06-22 15:50:49

Hi Fruityloop;

All I can say right now, is that seems close to the right answer. So good work!
You are correct in saying if might need computer assistance. All the math ideas I am
trying are really hard work.

bobbym · 2010-06-22 22:36:40

Hi;

Problem:

7 7 7 7 7 7 7 = 14 You must use each of + - / * once and only once.

A says) Can't be done, I need to concantenate those 7's
B says) That is implied, so it can be done.
C says) I am forced to agree with whatever D is going to say.
D says) I think it has lots of solutions.

Find the solution if you disagree with A:

bobbym · 2010-06-24 22:01:23

Anakin wrote:

A tool shed, 250 cm high and 100 cm deep, is built against a wall. Calculate the shortest ladder that can reach from the ground, over the shed, and to the wall behind.

A says) This guy solved it using Calculus, that is the right way. http://www.mathisfunforum.com/viewtopic … 82#p145382
post #2. That guy is good!
B says) He is okay but he is too mechanical. There is a nice computer way to solve that, No Calculus allowed.
C says) I agree with A.
D says) You don't need a computer either, just a large sandy beach.
E says) Man, I love the beach.

Who is right and why?

bobbym · 2010-06-29 17:37:50

A box of max.

B has 10 cards and on them he writes 10 positive numbers. He looks at the cards and says , if you sort them in descending order
a > b > c > d > e > f > g > h > i > j , then b + c > a and d + e + f > b + c > a and j + i + h + g > d + e + f > b + c > a. then there is the a smallest a and a largest j.

A says) Impossible.
B says) No it isn't.
C says) I have the answer.
D says) But A is never wrong.
E says) I agree with D.

Who is right?

bobbym · 2010-07-03 00:00:39

So easy, it hurts to write it!

When can you draw a tangent from a point to a parabola?

A says) There is always a tangent from any point to any parabola! I have a 29 page proof of this.
B says) As usual A has gone off on a tangent. You can't draw a tangent from just any point to a given parabola.
C says) It is hard to believe but A is wrong.
D says) I agree with A, I have been drawing paraboli all day and I can't find a single point that you can't draw a tangent from.
E says) I agree with B, I am sure you can find an example of a point and a parabola that you cant draw a tangent to the parabola and through the point.

Who is right and can you find the conditions when you can and can't?

rga1015 · 2010-07-14 20:20:26

hi... pls show the complete solution.... what is the derivative of f(x)=square root of (4x^2-1)

bobbym · 2010-07-14 20:26:27

Hi rga1015;

Use the chain rule.

Say

Now just plug into A)

Welcome to the forum!

jimmyR · 2010-07-15 16:18:26

Hi bobbym;

Last edited by jimmyR (2010-07-15 16:20:14)

bobbym · 2010-07-15 16:21:50

Hi jimmyR;

Thanks, I know that one!

phrontister · 2010-07-26 03:01:14

Hi Bobby,

Re your post #285:

Do you think you can come up with a solution method using 7? A method that LB couldn't do?

Finally got around to looking at this. No time!

I guess you mean using a 'permutations' function (which LB doesn't have in-built). I used the 7 formula you gave me and solved it like

My LB code only takes about 4.5 seconds, but I cheated by whittling down the options with some logic to the point where LB was left with very little to do.

my code.

I also remembered a problem that a LB forum member helped solve for me about a year ago. It contained a permutations function, which I've adapted for this puzzle. Speed is about 10x faster than my old full code, but 7 is about 10x faster again.

the code.

My code is very wordy, but I like to get reasonable output presentation and also to weed out non-solutions.

Soon I'm going to reinstall my old 2.7GHz dual core processor as it's generally faster than the 3.2GHz quad I had installed recently. About the only benefit I've seen with the quad is in video rendering (my reason for getting it), which I did a lot of for a few weeks after my last holiday...but the general slow-down (especially with Excel, LB & 7, where the dual core is 3x faster!) is annoying. I should have researched it better before buying it.

Last edited by phrontister (2010-07-26 03:38:32)

bobbym · 2010-07-26 03:54:49

Hi phrontister;

Where the heck have you been? That is nasty good code!

Have you got M set to utilize the extra processors?

phrontister · 2010-07-26 11:36:57

Hi Bobby,

The death of a 90-year-old close member of the family has made life even more hectic than it already was, and I just can't keep up with everything that needs doing. I've had to cut down my forum participation (not just MIF) to cope.

Thanks for that optimizing hint. It worked, and processing time for the puzzle on M is down to about a fifth of previous. 3 cores ran at >90% for the whole process, while the other ran at about 80%. It warmed up the cpu by a couple of degrees...so I can save on wood for the fire!

EDIT: The Timing function doesn't work properly now that I changed the code to include Parallelize, and in fact the processing time is only down to half of what it was before parallel optimization. The timer always worked well before.

my new code.

I think I'll still go ahead with the cpu swap, though, because most of the old programs I run can't be optimized for quad and I don't want to keep the quad just for the couple that can be optimized. Those old programs, and my computer generally too, all run slower now, and until I upgrade most of them (but that's $$$!) - and provided they take advantage of parallel processing - I'll be better off with dual core. I've read up about it, and that seems to be the consensus.

Last edited by phrontister (2010-07-27 10:51:26)

bobbym · 2010-07-26 16:39:06

Hi phrontister;

Sorry about your loss. I lost my mom in november, so I know what you are going through. Helps to work, particularly on problems that have nothing to do with everyday existence.

Good use of the Parallelize command. I think their is a switch in M in the options to make sure that you use your multiple cores more efficiently. Anyway, you might be right to switch back.

Again, I offer my condolences to you, hope you recover quickly.

Math Is Fun Forum

#301 2010-06-09 05:04:27

Re: What do you think?

#302 2010-06-09 07:55:45

Re: What do you think?

#303 2010-06-09 12:06:52

Re: What do you think?

#304 2010-06-09 13:04:47

Re: What do you think?

#305 2010-06-10 02:32:17

Re: What do you think?

#306 2010-06-10 03:05:50

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#307 2010-06-16 21:25:17

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#308 2010-06-16 22:11:33

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#309 2010-06-16 22:30:15

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#310 2010-06-16 22:48:54

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#311 2010-06-16 23:07:55

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#312 2010-06-22 12:38:38

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#313 2010-06-22 15:50:49

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#314 2010-06-22 22:36:40

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#315 2010-06-24 22:01:23

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#316 2010-06-29 17:37:50

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#317 2010-07-03 00:00:39

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#318 2010-07-14 20:20:26

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#319 2010-07-14 20:26:27

Re: What do you think?

#320 2010-07-15 16:18:26

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#321 2010-07-15 16:21:50

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#322 2010-07-26 03:01:14

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#323 2010-07-26 03:54:49

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#324 2010-07-26 11:36:57

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#325 2010-07-26 16:39:06

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