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Straight Lining


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18 replies to this topic

#1 superprismatic

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Posted 25 August 2012 - 11:02 PM

I recently read an article in the American Mathematical Monthly,
August-September 2012, about straight line programs. The article,
by Peter Borwein and Joe Hobart, was about how these things would be
affected by allowing the division operation. But a rather simple idea
for a puzzle formed in my head after reading it. So, here it is:

A straight line program is a sequence of integers p1,p2,p3,....,pn
such that p1=1 and pi is the sum, difference, or product of pk and pl
where k and l are both less than i. It is OK if k=l. So, for example,
one possible straight line program which ends in 12 is 1,2,4,3,12. To be
explicit, p1=1, p2=p1+p1, p3=p2+p2, p4=p3-p1, p5=p4*p3.

Find a shortest straight line program ending in 137.
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#2 phil1882

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Posted 26 August 2012 - 03:52 AM

Spoiler for

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#3 CaptainEd

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Posted 27 August 2012 - 01:28 AM

oops, another senior moment...
Except I admire the problem and Phil's solution!

Edited by CaptainEd, 27 August 2012 - 01:30 AM.

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#4 TheChad08

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Posted 27 August 2012 - 04:37 AM

Yeah, I can't get better than Phil's.
I can tie it if I am allowed to use division.
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#5 phil1882

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Posted 27 August 2012 - 09:58 AM

how about this tie sequence...
Spoiler for

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#6 TheChad08

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Posted 27 August 2012 - 07:23 PM

how about this tie sequence...

Spoiler for

How'd you get from the 5 to the 9 in one move?
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#7 phil1882

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Posted 27 August 2012 - 07:47 PM

3*3 = 9, you're allowed to use any combination of previous values to get the next one.
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#8 CaptainEd

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Posted 27 August 2012 - 09:07 PM

Spoiler for Another tie

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#9 superprismatic

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Posted 28 August 2012 - 01:11 AM

Nice going, guys! If you'd like to try another, I think that 277 is pretty hard.
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#10 CaptainEd

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Posted 28 August 2012 - 04:45 AM

Spoiler for 1 plus 7 steps, like the other one


Phil taught me all I know...

Edited by CaptainEd, 28 August 2012 - 04:47 AM.

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