Power-Ball Lottery

Explorers who know math know that playing the lottery is dumb.  The chances of winning are almost always lower than the amount you win. But today, January 12, 2016, the winning amount is $1.5 billion! Even after taxes, the odds are in your favor because there's a 1 in 292 million chance of winning. However, if there are two or more winners and you have to split the pot, the odds then become dumb again.

So this math-wise explorer is not playing the lottery and did not buy a ticket.  But if he did, he would have picked these five white-ball numbers: 12, 13, 36, 43 and 57 and for the red power ball: 5.

Let's see if he regrets not buying a ticket worth over a billion dollars!

UPDATE: Upon further reflection, if those numbers DO win, I'm going to feel like an idiot and I hate that feeling! So I bought a single ticket with those numbers. And just to make it more fun, I'll share the money with anyone who can tell me the exact number of possible tickets in the Powerball. The rules are: all five white balls (1 to 69) have to match, but they can be in any order, and the red ball (1 to 26) has to match.  Good luck!

Exact number of possible tickets:

Solve this problem to get one million dollars!
 

Stuck on Kolepom Island

Over your Christmas vacation, you decided to go on an expedition to Kolepom Island because you heard there was a sighting of Attenborough's echidna there! Unfortunately, soon after you arrived at the village to meet your guide, the chief of the tribe took your weapons and locked you in a hut.

It seems the chief will not deal with any Westerners unless they prove that they respect the tribe's culture. He has given you the problem below to prove your worth. If you can solve it before the sun sets, he will be your personal guide to find Attenborough's echidna which he claims to have seen with his own eyes. But if you fail, you will be cooked and eaten at their annual feast of the echidna in three days time.

Good luck!