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 The not-always-lying politician (Posted on 2004-02-27)
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 polite solution | Comment 10 of 20 |

(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
 Posted by Penny on 2004-02-28 08:04:16

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