There happens to be a politician that might lie at any moment (this isn't unusual) but his conscience bothers him enough (now,
that is unusual!) so he won't say two lies in a row.
He said ten consecutive statements.
How many combinations of truths/lies can there be?
(Clever pun, Mr. Porter.....)
There are 144 ways for the pol to tell no consecutive lies in 10 statements.
Explanation
He can tell at most five lies.
Zero lies
1 possibility
One lie
10 possibilities
Two lies
1+2+3+4+5+6+7+8 = 36 possibilities
Three lies
1+(1+2)+(1+2+3)+(1+2+3+4)+(1+2+3+4+5)+(1+2+3+4+5+6) = 56 possibilities
Four lies
1+(1+[1+2])+(1+[1+2]+[1+2+3])+(1+[1+2]+[1+2+3]+[1+2+3+4]) = 35 possibilities
5 lies:
1+2+3 = 6 possibilities
1+10+36+56+35+6=144
Edited on March 1, 2004, 11:39 pm
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Posted by Penny
on 2004-02-28 08:04:16 |
A polite solution
