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The not-always-lying politician (Posted on 2004-02-27) Difficulty: 3 of 5
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?

See The Solution Submitted by Federico Kereki    
Rating: 4.0000 (5 votes)

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a gross solution | Comment 9 of 20 |
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
  Posted by Dan Porter on 2004-02-27 17:40:47
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