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Guest Message by DevFuse

The well-ordered orchard

Started by bonanova, Feb 15 2013 06:09 AM

Best Answer bonanova, 08 April 2013 - 06:28 AM

Time to plant the trees.

Assuming interest on this puzzle is spent, let's close it out.

Spoiler for Eighteen rows of 3

Honorable mention to plasmid, whose last post was clearly on the right track.

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22 replies to this topic

#1 bonanova

bonanova

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Posted 15 February 2013 - 06:09 AM

The gardener planted his orange trees in a superbly ordered manner.

Not counting pairs of trees as a "row", he created nineteen rows of trees.

How many trees was it necessary for him to plant?

0

The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

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#2 CaptainEd

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Posted 15 February 2013 - 04:21 PM

Spoiler for oops, I planted too many

Edited by CaptainEd, 15 February 2013 - 04:24 PM.

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#3 CaptainEd

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Posted 15 February 2013 - 04:35 PM

Spoiler for a solution

Edited by CaptainEd, 15 February 2013 - 04:38 PM.

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#4 bonanova

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Posted 15 February 2013 - 05:47 PM

Spoiler for a solution
Spoiler for 18 trees
A   B   C
E   F   G   H
I   J   K   L
M   N   O   P
    R   S   T
5 horizontal rows
4 vertical columns
4 diagonals with slope 1 (ROL, NKH, MJG, IFC)
4 diagonals with slope -1 (SNI, TOJE, PKFA, LGB)
2 knight's move diagonals with slope -2 (AJS, BKT)

Nice, and extremely well ordered.
But the gardener was more frugal. He used fewer trees.

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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

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#5 CaptainEd

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Posted 15 February 2013 - 05:52 PM

Wow! His name wasn't Martin, was it?

Please correct me if I'm wrong: a line of 4 counts as one row of 4, rather than two rows of three, right?

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#6 CaptainEd

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Posted 15 February 2013 - 06:19 PM

I see your point

Spoiler for better still

Edit: from "more frugal" to "better still" that meets the OP with even fewer trees

Edited by CaptainEd, 15 February 2013 - 06:26 PM.

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#7 bonanova

bonanova

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Posted 15 February 2013 - 07:13 PM

Wow! His name wasn't Martin, was it?
Please correct me if I'm wrong: a line of 4 counts as one row of 4, rather than two rows of three, right?

Sometimes it's Martin, a semi-idol of mine, but not this time.
It's gardener, lower case, with two "e"s.

Correct. A row of four is not also two (or four) rows of three.
A row is a row, and its size is the number of trees aligned with it.

Clue:
If the rows of length greater than three are excluded, there are (only) eighteen rows.