# The truth and lie mess

There are two persons with special traits such that :

• One speaks only lies and no truth on Monday, Tuesday and Wednesday and all truth rest of the week.
• The other speaks only lies and no truth on Thursday, Friday, Saturday and all truth rest of the week.

They both meet up at a coffee shop, What is the probability that both will say "I spoke a lie yesterday"??

Quite simple puzzle but yet fun.

The probability is

$\frac{1}{7}$

For the first person :

Monday : The fact that he said a lie yesterday is wrong but he is lying so he can say "I spoke a lie yesterday"
Tuesday / Wednesday : The fact that he said a lie yesterday is true and he he lying so he can't say it
Thursday : The fact that he said a lie yesterday is true and he says the truth so he so he can say it
Friday / Saturday / Sunday : The fact that he said a lie yesterday is wrong and he says the truth so he so he can't say it
---> He can only says this sentence on Monday and Thursday

For the second person :

It's the same but with a 3 days shift so he can say this only on Thursday and Sunday.

The probability is :

$\frac{1}{7}$ which is the probability that they meet on Thursday

Note that :

this assume that they speak every day

• Bingo!! was expecting to be answered in a few mins May 29 '16 at 12:46