## Welcome to BrainDen.com - Brain Teasers Forum

 Welcome to BrainDen.com - Brain Teasers Forum. Like most online communities you must register to post in our community, but don't worry this is a simple free process. To be a part of BrainDen Forums you may create a new account or sign in if you already have an account. As a member you could start new topics, reply to others, subscribe to topics/forums to get automatic updates, get your own profile and make new friends. Of course, you can also enjoy our collection of amazing optical illusions and cool math games. If you like our site, you may support us by simply clicking Google "+1" or Facebook "Like" buttons at the top. If you have a website, we would appreciate a little link to BrainDen. Thanks and enjoy the Den :-)
Guest Message by DevFuse

# Straight Lining

18 replies to this topic

### #1 superprismatic

superprismatic

Not just Prismatic

• Moderator
• 1281 posts
• Gender:Male

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.
• 0

### #2 phil1882

phil1882

Senior Member

• Members
• 564 posts

Posted 26 August 2012 - 03:52 AM

Spoiler for

• 0

### #3 CaptainEd

CaptainEd

Senior Member

• Members
• 1094 posts

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.

• 0

• Members
• 180 posts

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.
• 0

### #5 phil1882

phil1882

Senior Member

• Members
• 564 posts

Posted 27 August 2012 - 09:58 AM

Spoiler for

• 0

• Members
• 180 posts

Posted 27 August 2012 - 07:23 PM

Spoiler for

How'd you get from the 5 to the 9 in one move?
• 0

### #7 phil1882

phil1882

Senior Member

• Members
• 564 posts

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.
• 0

### #8 CaptainEd

CaptainEd

Senior Member

• Members
• 1094 posts

Posted 27 August 2012 - 09:07 PM

Spoiler for Another tie

• 0

### #9 superprismatic

superprismatic

Not just Prismatic

• Moderator
• 1281 posts
• Gender:Male

Posted 28 August 2012 - 01:11 AM

Nice going, guys! If you'd like to try another, I think that 277 is pretty hard.
• 0

### #10 CaptainEd

CaptainEd

Senior Member

• Members
• 1094 posts

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.

• 0

#### 0 user(s) are reading this topic

0 members, 0 guests, 0 anonymous users