perplexus.info :: Numbers : More chameleons

More chameleons (Posted on 2002-07-30)

Long ago, there existed a species of fighting chameleons. These chameleons were divided into six types of matching color and strength:

Black were the strongest, followed by

blue,

green,

orange,

yellow and

white which were the weakest.

Whenever two chameleons of the same color met, they would fight to the death and the victor would become stronger and change color (eg white to yellow). Black chameleons would fight eternally.

The small island of Ula was initially populated by a group of fighting chameleons. For this group

a) the colors present each had an equal number of chameleons (for example, group = 3 black, 3 green and 3 yellow)

b) it was not made up entirely of white chameleons

After all the possible fighting was done, there remained one black and green and no blue or orange chameleons.

How many white chameleons remained in the island? Prove it.

Submitted by Cheradenine

Rating: 3.5000 (14 votes)

Solution: (Hide)

The island of Ula is really a huge adding machine, whose basic mechanism is chameleons. Once youve realised this, its a matter of translation (:)
a): all the number added are equal. this type of addition has a name, multiplication:
chameleons per color * colors present = survivors n * c = s
b): c != 1 (im using != as not equal)
"After all the fighting..": n != 1.
We know that s = 1010XX, s = 101000-101011 = 40-43. 41 and 43 are prime, and s = n * c. since n != 1 != c, s != 41,43
so s = 40, 42 = 101000, 101010.
No white chameleons left, regardless of yellow.
You can also prove this systematically, by obtaining all initial combinations which result in 1010XX and finding all with white = 0. This would inadvertently prove that 41,43 are prime.
Btw, confusion aside, i dont think this puzzle deserved a rating of 1 :)

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
re: my apologies	LigiaOzimek	2021-10-04 08:03:08
Answer	K Sengupta	2008-03-15 05:08:34
Solution	Dej Mar	2007-05-03 23:51:30
re(4): Duh!	tomarken	2006-03-02 16:15:34
re: I must be missing a big part of the puzzle...	john	2005-06-08 17:08:14
re(3): Duh!	john	2005-06-08 16:57:31
I must be missing a big part of the puzzle...	Erik O.	2005-01-12 15:44:54
Oops	Gautam	2003-01-21 16:21:28
My Answer	Gautam	2003-01-21 15:06:45
re(2): Duh!	kyle	2003-01-08 18:04:37
re: Duh!	TomM	2002-07-30 16:29:44
Duh!	Emma	2002-07-30 11:34:05
re(2): solution	lucky	2002-07-30 05:37:41
re: solution	Cheradenine	2002-07-30 04:49:00
re(3): solution (explanation)	levik	2002-07-30 04:46:55
re(2): solution (explanation)	TomM	2002-07-30 04:13:09
solution	TomM	2002-07-30 04:04:41
Numbers	Nick Reed	2002-07-30 02:07:32
my apologies	Cheradenine	2002-07-29 22:09:01
Perhaps...	levik	2002-07-29 20:28:41
re(3): change wording..	TomM	2002-07-29 17:55:18
re(2): change wording..	Nick Reed	2002-07-29 13:58:47
re: change wording..	levik	2002-07-29 09:00:24
change wording..	Cheradenine	2002-07-29 07:34:48
Any number?	Ender	2002-07-29 07:03:10
re: What am I missing?	Cheradenine	2002-07-29 06:59:51
What am I missing?	Nick Reed	2002-07-29 06:41:52

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