Actual interview brainteaser at a top flight shop

[sjfan]

You win the first time three heads show up. So, if head = 1 and tail is 0, and the following is the sequence of flips:

111 -> you win
1011 -> you win
0111 -> you win
01011 -> you win

000 -> you lose
1000 -> you lose
10100 -> you lose

Does this make sense where the 3 heads you win and 3 tail you lose comes in? you get to bet before each flip. you want to double your initial stake whenever you win

Quote from Anaconda:

Explain this.

You can bet per flip so what's the point of the 3 heads? That ends the game and doubles your bank (which you called stake).?

 

[sjfan]

Just to be clear: whether you win or not is not up to you (it's a fair coin after all). But when you win, you need to double. That's the requirement. (Don't care what happens when you lose, but in the correct solution, a very logical thing happens)

Quote from AyeYo:

Winning the game is different than meeting your goal. It's a game within a game. You need to win the game AND double your money while doing it. You can win the game and lose your money. You can double your money and lose the game. You need to win AND double. That's the brainteaser part.

 

[Anaconda]

Quote from sjfan:

Just to be clear: whether you win or not is not up to you (it's a fair coin after all). But when you win, you need to double. That's the requirement. (Don't care what happens when you lose, but in the correct solution, a very logical thing happens)

That clears it up. You have to assume you win.

 

[KarateChop]

Quote from sjfan:

No dice. Suppose the flip outcome is tail tail head tail head head?

you lose 50, lose 25, win 50 (so now your stack is $75). You can't bet $100 on the last cause you don't have it

Huh? I thought it was only being flipped 5 times? You just posted an example with 6 flips?

 

[sjfan]

Apologize. I did type out a loss scenario.

Try this, tail head head tail head

-50, +25, +25, -50 = -50. This means your stake is now $50. you can't bet $100 on the final round

Quote from KarateChop:

Huh? I thought it was only being flipped 5 times? You just posted an example with 6 flips?

 

[Pension_Admin]

"Question: what is the size of the first bet that you should make?"

I am thinking $50 on the first bet and 50% of the accumulated capital on the subsequent bet.

I don't have any mathematical proof, but I have attached an Excel file to simulate the flips.

 

[Bogwaluth]

I came up with $50 as well. You bet half your stack at all times unless you have $100 and 1 roll left, at which time you bet it all.

How long would you have to answer that type of question in an interview?

 

[sjfan]

What happens if you have tail, head, tail, head, head?

Round 1. Bet $50, tail, = $50
Round 2. Bet $25, head = $75
Round 3. Bet $37.5, tail = 37.5
Round 4. Bet 18.75, head = 56.25
Round 5. Bet 28.125, head = 84.375

You fall short of $200 even though you won the game.

Quote from Pension_Admin:

"Question: what is the size of the first bet that you should make?"

I am thinking $50 on the first bet and 50% of the accumulated capital on the subsequent bet.

I don't have any mathematical proof, but I have attached an Excel file to simulate the flips.

 

[sjfan]

Incorrect for the reasons already stated.

The typical interview is an hour. I would expect to reserve a good 20 min for the preliminaries and questions. So figure 40 min?

But keep in mind, you might be given some hints if you look completely lost or confused. I'll give a few hints as time goes on to simulate that.

Speaking of which,

HINT #2: If you already seen two heads and you are in your final bet, and the outcome is going to head (so you double your bet), what's the minimum amount of money you need to have on hand to meet the required payout? (don't need to reply with an answer. this is a hint question)

Quote from Bogwaluth:

I came up with $50 as well. You bet half your stack at all times unless you have $100 and 1 roll left, at which time you bet it all.

How long would you have to answer that type of question in an interview?

 

[Bogwaluth]

Quote from Bogwaluth:

unless you have $100 and 1 roll left, at which time you bet it all.

That's why I added the part above. On your t,h,t,h,h scenario you get

Bet 1 - 50 / New Bank Roll - 50
Bet 2 - 25 / New Bank Roll - 100
Bet 3 - 50 / New Bank Roll -50
Bet 4 - 25 / New Bank Roll - 100
Now use the exception to the strategy above and
Bet 5 100 / New Bank Roll - 200