# Can you solve this?

Discussion in 'Community' started by mms, Dec 9, 2004.

1. ### mms macrumors 6502a

Joined:
Oct 8, 2003
Location:
CA
#1
Solve a strategy problem, in which there is a game. The objective is to get to the number 50 first, and it is for 2 players. The first person can choose a number between 1 and 10, and the second person can choose a number 1 to 10 numbers away from the chosen number. With this information, what is the best number to choose first if you are the first person to go?

Present your logic as well. This is reportedly a problem from a management consultant's application.

2. ### emw macrumors G4

Joined:
Aug 2, 2004
#2
I'm no genius, but here's my reverse engineering of the problem.

First, the goal really is to get to 39 first. If you get to 39, then the other person has to go to at least 40, which means you can win no matter what number is added to your 39.

Which means you never want to be the one who adds to 29, because then your opponent jumps to 39 and you lose.

Which means you never want to be the one who adds to 19, because then your opponent picks 29, you have to go to at least 30, your opponent adds 9 to get to 39 and you lose.

Which means you want to be the first to add to 18. If you get to 18, then you can't lose. Because your opponent will have to add at least 1 to get to 19 and at most 10 to get to 28. Either way, you can add to get to 29. He has to add to at least 30, so you can always be first to 39, which means he can never be more than 49, and you will always get to 50 first.

So how do you get to 18 first most efficiently? Pick 7. You opponent will have to add at least 1, getting him to 8, so you can add 10 to get to 18. If he adds 10 (to get to 17), you add 1 to get to 18. From there, see the previous paragraph.

I'm sure there's a mathematical formula somewhere, but I'm too lazy.

3. ### aus_dave macrumors regular

Joined:
Jan 6, 2004
#3
Maybe not emw, but you made sure this thread doesn't get much longer!

Nice logic .

4. ### Mr. Anderson Moderator emeritus

Joined:
Nov 1, 2001
Location:
VA
#4
What really gets me is that this is actually a question on an application

If it was for a management position, right? The correct answer would be to give it to someone else to solve....

D

### Staff Member

Joined:
Feb 5, 2004
Location:
New Zealand
#5
Slight mistake there

However, your logic is correct, just keep subtracting 11 from 50 (39, 28, 17, 6). So you'd want to choose 6, which is just the remainder when dividing 50 by 11.

6. ### jsw Moderator emeritus

Joined:
Mar 16, 2004
Location:
Andover, MA
#6
Choose φ (phi). No other applicant for a management position will know what it is and so will never really know what the total is or when it gets within 10 of 50.

Actually, since "number" and not "whole number" was used, you could get within (40 - (1/∞ )) and still be safe. So I'd say pick (10 - (1/∞ )) as your first value, and keep ensuring that the value is ((n*10) - (1/∞ ) ) until your opponent bumps it to (41 - (1/∞ )) or higher (they need to increment it by at least 1), then you win on the next play.

Edit: No, never mind. That minimum-value-of-1 jump could screw you as well if you did that....

7. ### emw macrumors G4

Joined:
Aug 2, 2004
#7
Doh! Never get up to put your daughter back in bed in the middle of something like this! I didn't even re-read to catch such a blatant mistake. Ah, well, that's why you're the real genius. I had the logic, but got lost in my effort to be verbose.

8. ### jsw Moderator emeritus

Joined:
Mar 16, 2004
Location:
Andover, MA
#8
Ah, but using faulty logic to try to sell a solution which you're convinced is correct is fundamental to management consulting.

Perhaps the best management consultant answer would be "Pick 50 and fire the guy who said I had to start with anything less than the winning position."

### Staff Member

Joined:
Sep 19, 2002
Location:
Los Angeles
#9
This is a one-heap version of the game of Nim, of which there are many variations. The solution follows the same pattern. One of the first BASIC programs I ever wrote when learning to program was an interactive program to play Nim. You played against the computer and the computer played perfect strategy. If you wanted to beat it, you had to be perfect too, in which case the random choice that determined which player went first would determine the winner, since either the first player or the second player could force a win in a given game.

10. ### Chappers macrumors 68020

Joined:
Aug 12, 2003
Location:
At home
#10
Actually get two people to do it, then when you have an answer make sure you take the credit for it.

11. ### Jaz macrumors regular

Joined:
Sep 7, 2004
Location:
Sydney, Australia
#11
Speaking as a former Big 5 Consultant (Deloitte), this guy wins

Management consulting firms love these things. When I did my application we had to do an online logic test as part of it. 45 questions, 30 minutes, various logic problems etc.

However jsw came closest to what it's actually like when you're finally in a firm.

12. ### virividox macrumors 601

Joined:
Aug 19, 2003
Location:
Manila - Nottingham - Philadelphia - Santa Barbar
#12
HAHa brilliant!!!

### Staff Member

Joined:
Sep 19, 2002
Location:
Los Angeles
#13
This is a good test question for a potential manager:

Which of these two would you hire: a consultant who answered yes/no questions correctly 70% of the time or a consultant who answered yes/no questions correctly 20% of the time?

14. ### jxyama macrumors 68040

Joined:
Apr 3, 2003
#14
i assume the answer is to hire the latter guy and do the opposite..?

(but then you'll need to pray and make sure that he doesn't wise up and start getting the right answers..)

15. ### CubaTBird macrumors 68020

Joined:
Apr 18, 2004
#15
perhaps the question to mms' management application

16. ### emw macrumors G4

Joined:
Aug 2, 2004
#16
My thought would be why are you asking yes/no questions in the first place? You seldom get good information (especially from a consultant) by asking yes/no questions.

### Staff Member

Joined:
Sep 19, 2002
Location:
Los Angeles
#17
That's the beauty of hiring a consultant: the minute you don't like the work (in this case, because he/she got better at producing correct answers), you dump him and get another consultant (or a Magic 8-Ball).

18. ### kjr39 macrumors 6502

Joined:
Nov 26, 2004
#18
Assuming the latter consulant is like me, the first word out of my mouth when asked a yes/no question is usually "Depends." To which I give a lengthy answer to why it may be yes, but under certain circumstances could be no...