# The Critical Line – Volume 15

Can you find your way squarely around this month’s puzzle? Jevon Fulbrook challenges you to spell out the enigma for a chance to win a $50 Dymocks voucher.

The following puzzle was inspired by a fantastic website shared with me recently by a reader. Despite the puzzle design not being original, the actual puzzle itself is!

Within the grid below, you’re asked to draw a path connecting the centres of horizontally and vertically adjacent squares. Your path should form a single loop that neither touches nor crosses itself, but that passes through each shaded cell in the grid.

The loop, if completed correctly will leave 15 letters remaining which will spell out the solved enigma!

Send your solution in to **ActuariesMag@actuaires.asn.au** to go in the running to win a $50 Dymocks voucher!

**Critical Line Volume 14 Solution**

by Dan Mayoh (dan@fintega.com):

Part A:

The probability of any given person winning the jackpot in a given hand is 4 / (52 Choose 5).

The probability of any of the 10 players in the hand winning is simply 10 times this (note that the probability of more than 1 person winning in the same hand is 0). So the answer to part A is 1 in 64,974.

Part B: This is simply 64974 * 10 seconds, which is 7 days, 12 hours and 29 minutes

Part C:

The answer is $14,619.15, which happens to be 64974 * $0.15 * (1/(1 – 1/3)). There are a few different ways to derive this as the answer.

What is interesting to note about this question is that:

- The initial value of $10,000 is irrelevant.
- The precise stopping time of midnight on Dec 31 is irrelevant – any point in time a sufficient length of time away from the start (say 3 months or more) would have the same expected value
- The long term expected value of the jackpot size at any moment in time is the same as the long term expected value of the next jackpot won. This makes sense when we consider that the jackpot is equally likely to be won on any hand, regardless of how long it has been since the last win or what the value of the jackpot is.

Congratulations to Andrew Parker who submitted the only correct solution, and wins the book voucher!

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