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 Gardener's Woe (Posted on 2006-06-24)
An unlucky gardener planted a 10x10 square array of 100 old seeds out in the garden. Only 5 of these seeds have germinated including one at the southwest corner (0,0) where a slug is currently reducing it to ground level.

When it finishes it will head directly to the next closest doomed plant. After it eats that one it will again leave a slime trail to the closest remaining plant and so on until the garden is no more.

Where are the 4 remaining seedlings if the path crawled by the slug is the longest possible and it never has to choose between two equidistant snacks?

Note: Although the slug will never have to choose between two equidistant seedlings, this doesn't imply that no two are equidistant.

Next find the locations if 6 seedlings had germinated instead of 5.

 See The Solution Submitted by Jer Rating: 4.0000 (1 votes)

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 computer solution for 5 | Comment 16 of 26 |

DECLARE SUB place (lvl!)
DIM SHARED n
n = 5
DIM SHARED curX(n), curY(n), curDist(n), curTot(n)
DIM SHARED hldX(n), hldY(n), hldDist(n), hldTot

curX(1) = 0
curY(1) = 0
curDist(1) = 0
curTot(1) = 0

place 2

END

SUB place (lvl)
FOR r = 0 TO 9
FOR c = 0 TO 9
FOR pLvl = 1 TO lvl - 2
dist = SQR((r - curY(pLvl)) * (r - curY(pLvl)) + (c - curX(pLvl)) * (c - curX(pLvl)))
IF dist <= curDist(pLvl + 1) THEN GOTO notThis
NEXT pLvl
dist = SQR((r - curY(lvl - 1)) * (r - curY(lvl - 1)) + (c - curX(lvl - 1)) * (c - curX(lvl - 1)))
IF dist = 0 THEN GOTO notThis
curX(lvl) = c
curY(lvl) = r
curDist(lvl) = dist
curTot(lvl) = curTot(lvl - 1) + dist
IF lvl = n THEN
IF curTot(lvl) > hldTot THEN
FOR i = 1 TO n
hldX(i) = curX(i): PRINT hldX(i);
hldY(i) = curY(i): PRINT hldY(i); "   ";
hldDist(i) = curDist(i)
NEXT
hldTot = curTot(lvl)
PRINT hldTot
END IF
ELSE
place lvl + 1
END IF
notThis:
NEXT c
NEXT r
END SUB

ultimately finds

0  0      6  5      9  9      9  0      0  8     33.85184

 Posted by Charlie on 2006-06-25 15:07:10

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