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Guest Message by DevFuse

Straight Lining

Started by superprismatic, Aug 25 2012 11:02 PM

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18 replies to this topic

#1 superprismatic

Not just Prismatic

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1196 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,....,p_n
such that p₁=1 and p_i is the sum, difference, or product of p_k and p_l
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.