rec.puzzles Archive

How can you plant three unidentifiable tulip bulbs (blue, white, red) so that the flowers are sure to show...

logic/tulip.bulbs New

New entry, edited from material collected for the archive and not yet in a released version.

Problem

How can you plant three unidentifiable tulip bulbs (blue, white, red) so
that the flowers are sure to show blue, white and red from left to right?

The greasy, stinking peasant oozed his way into the King's audience
chamber and boldly demanded that he be allowed to marry the princess.
Having seen the historical inevitability of democratic reforms, and not
wanting to injure his own chances of being elected El Presidente, the
King decided to give the odious ratbag a chance, rather than just
instantly offing him as would have happened in The Good Old Days.

So the King brought the filthy, cankerous peasant to a room containing a
dirt-filled pot and three tulip bulbs which were all identical to any
form of inspection available in that era.

"One of these bulbs will grow into a flower with blue petals, another
into one with white petals, and the third into one with red petals.  I
want you to plant these three bulbs in this pot such that, when they
bloom, I will see the royal colors in their proper order, which is blue,
white and red, from left to right."

The festering, putrid peasant thought about it for a minute, then set
about planting the three bulbs in the pot.  As he was licking his hands
clean of dirt, the guards dragged him off to the dungeons and the pot
was placed in the care of the Royal Gardener, who was utterly loyal to
the King and completely incorruptible.

Months later, with the arrival of spring, the King had the slimey
peasant brought before him once more.  "The Royal Gardener tells me that
the tulips have now bloomed.  Go bring the pot before me and we shall
see whether you live or die.  Oh, and to make sure that you cannot
change the ordering of the flowers along the way, I am sending Algor, my
loyal and completely incorruptible guard, along to make sure that there
are no shenanigans."

When the foul, depraved peasant finally returned with the pot, he set it
down triumphantly before the King and, sure enough, the flowers showed
blue, white and red, from left to right.  The King had no choice but to
let the peasant live, but he refused to hand over his daughter.
Instead, he foisted off on the miserable peasant one of the royal
beagles, which happened to be named `princess', and issued a Royal
Decree allowing peasants to marry beagles.

The case is still in litigation today, but the question remains: how did
the [insert your own adjectives] peasant get the flowers in the right
order?

-- Dean Edmonds <deane@gooroos.com>
Show solution
serc18@sasknet.sk.ca wrote:

    Plant them as if they were on the three points of a triangle on the
    surface of the soil.  Then, rotate the pot (after the flowers have
    bloomed) so that you have them in the order you want (all orders are
    possible, I think).

Of course.  You get all six permutations as follows:

 B    A B   B C    C     A    C A
A C    C     A    B A   C B    B
-----------------------------------------
ABC   ACB   BAC   BCA   CAB   CBA

ObPuzzle: If you had four bulbs to plant, how would you do it to
maximize the chances that you'd be able to produce the arrangement that
the king wanted?

-- Matthew Daly <mwdaly@kodak.com>

[ Editor: no answer to the four-bulb question was among the collected
postings. ]