# Heaven Puzzle Solution

**Episode #5 of the course “Challenging logic puzzles”**

According to probability 1/3 of the time, the door to heaven will be chosen, so 1/3 of the time it will take 0 days. 1/3 of the time, the 1-day door is chosen, of those, the right door will be chosen the next day. Similarly, 1/3 of the time, the 2 day door is chosen, of those, the right door will be chosen after the 2 days.

So lets say it will take N days. 1/3 of the cases are done in 0 days as before. 1/3 of the cases are 1+N. 1/3 are 2 + N.

N = 1/3 * 0 + 1/3 * (1 + N) + 1/3 * (2 + N)

N = 1 + 2N/3

Therefore, N/3 = 1 ; N = 3.

So it will take on average 3 days to reach to heaven.

**Recommended book**

**“Pocket Posh Logic: 100 Puzzles” byThe Puzzle Society**

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