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?
There is 1 combination with no lies and 10 combos with one lie.
There are only 8 positions with two lies because there now must be one truth.
(9*8)/2=36 combos
With three lies we are down to 6 positions of freedom.
(7*6+6*5+5*4+4*3+3*2+2*1)/2=56 combos
Now we are up to and four lies and down to 4 positions.
(1*5*4+2*4*3+3*3*3+4*2*1)/2=35 combos
There are 6 combos with five lies.
Total number of combinations is 1+10+36+56+35+6=144
That's "one gross" solution!
Sorry about the solution being in the title but I thought most people wouldn't get it until they solved it them selves. I guess I'm saying it's more of a hint than a solution. Besides I couldn't resist. ;8^)
Edited on February 27, 2004, 5:41 pm
a gross solution
