Here is a variant of the same problem: On the island of Alopecia the following facts are true:
1 . No two islanders have exactly the same number of hairs.
2. No islander has precisely 450 hairs.
3. There are more islanders than there are hairs on the head of any one islander.
What is the largest possible number of islanders on Alopecia?
2007-01-03 07:42:21 · 15 answers · asked by Anonymous in Entertainment & Music ➔ Jokes & Riddles
I am in the mood of doing riddles today, the answer is 450. here is the reasoning:
FACT 1: this establishes the cardinality constraint where there is a one-to-one mapping from the i-th person to the i-th number of hair. Of course you can map in every imaginable way, as long as it is one-to-one, otherwise two islanders could have the same number of hair; the easiest way is to map them in order. In other word, you can draw up 2 columns, first colum lists everyone on the island from 1 to N and second colum lists all possible number hairs on a person's head from 0( it is not 1, because number of hair can be 0 or more) to N-1. And there must be a one-to-one mapping from colum 1 to column 2. For example, Person 1 maps to 0 hair, Person 2 maps to 1 hairs, Person 450 maps to 449 hairs, and Person 451 maps to 450 hairs.
FACT 2: this forces the mapping from 451th person to 451th number of hairs, because the 451th person cannot have 450 hairs. This directly contradicts with FACT 3 that stipulates there are more islanders than are hairs on any one islander. Having finding out the upper bound of trouble spot, therefore, the largest possible number of islanders to make these 3 facts consistent is 450.
2007-01-03 09:58:24 · answer #1 · answered by M 3 · 0⤊ 1⤋
The largest possible number of islanders on Alopecia would be 450
2007-01-03 16:16:05 · answer #2 · answered by Poison 2 · 0⤊ 0⤋
As you cannot determine the most number of hairs any one islander can have, you cannot determine the largest possible number of islanders.
However, you do know that there is at least one islander, and if there is only one islander, then that islander is bald.
2007-01-03 16:49:14 · answer #3 · answered by ildjb@sbcglobal.net 5 · 0⤊ 1⤋
0 Hairs, 2 islanders?
2007-01-03 16:12:06 · answer #4 · answered by emzy_emz8 2 · 0⤊ 1⤋
450
2007-01-03 16:04:00 · answer #5 · answered by Anonymous · 0⤊ 1⤋
Alopecia means no hair I think
2007-01-03 16:05:12 · answer #6 · answered by Patches6 5 · 1⤊ 1⤋
328
2007-01-03 15:54:41 · answer #7 · answered by iputsugaronmysugar 2 · 0⤊ 1⤋
That would all depend on how many hairs are on Alopecia.
2007-01-03 15:50:47 · answer #8 · answered by Angelleena 1 · 2⤊ 1⤋
infinite minus 1
2007-01-03 15:50:19 · answer #9 · answered by Konrad 6 · 0⤊ 1⤋
every number besides 450 is possible
2007-01-03 16:30:48 · answer #10 · answered by Anonymous · 0⤊ 1⤋