# Thread: How do you think through this?

1. ## How do you think through this?

I'm curious how people work through this problem.

You are the general of an army of essentially infinite numbers. The opposing general has an army equally as massive. There are three battlefronts that will decide the war. A battlefront is won if you send as many or more troops than the opposing general and lost if you send less. To win the war you must win two of the three battlefronts. You sent your troops to the battlefronts in the magnitudes of 1/4 : 1/4 : 1/2 of your total army. The opposing general uses no strategy and distributes his troops randomly. What is the probability that you win the war?

2. Originally Posted by BlueGray
I'm curious how people work through this problem.

You are the general of an army of essentially infinite numbers. The opposing general has an army equally as massive. There are three battlefronts that will decide the war. A battlefront is won if you send as many or more troops than the opposing general and lost if you send less. To win the war you must win two of the three battlefronts. You sent your troops to the battlefronts in the magnitudes of 1/4 : 1/4 : 1/2 of your total army. The opposing general uses no strategy and distributes his troops randomly. What is the probability that you win the war?
This makes no sense... If the troops are infinite, how can you divide them?

3. i solve this by escaping from the army and let the idiots kill each others

4. I said essentially infinite. Basically there are too many for a single soldier to matter but still not infinite.

5. Originally Posted by BlueGray
I said essentially infinite. Basically there are too many for a single soldier to matter but still not infinite.
It's either infinite or it's not. There is no 'almost infinite'.

6. Logic is flawed. Can't work with 'near-infinite'. Now if you want to say "Both forces have equal resources and manpower", then we're getting somewhere.

Now:
If we know that there are 3 battlefronts, and the opposing force is randomly distributed, do we have intelligence as to the enemy distribution across the battlefronts?

Recon is vital in a war. So is strategy. Also, need lay of the land. If the enemy has the high ground, they'll expend less troops maintaining it than the opposing force would to capture it.

Given two equal forces, the force with the superior strategy should be victorious. Wars of attrition should be avoided. Personally, I want to see a layout of the war-zone, to include topology, enemy strongholds, and distribution of enemy forces, supply lines, etc....Anybody got a RISK board handy?

Couple of different possible strategies. My fav's for playing something like Risk are:
1.) Flank- Attack the enemy's weak point w/ 1 force. When they move to reinforce, move your flanking unit in to attack them from the back or the new weak point they've opened up.
2.) Spearhead- Concentrate your forces and run a wedge straight up the middle of the enemy. Keep reinforcing your 'blades' from the center. Drop units from center-rear to engage disjointed forces as you break the line and divide their forces.

If ya give me more to go on, I could pick the brains of a few retired officers, SF, and some door-kickers I know.

Also, needs more Sun Tzu and Musashi

7. What is the stregic value of each of the three battlefields? Are they all equal in value? If so, you can assume that the other side will distribute 1/3 of troop total to each front. If not, you can use that to your advantage, if you know in advantage what the values are.
but you still need to know more rules of the game to win it.

8. The point of saying near infinite is that the numbers become incredibly messy when dealing with a finite size but they do approach simpler numbers. It's basically asking for the limit as the number of troops approach infinity.

9. Originally Posted by nebbykoo
What is the stregic value of each of the three battlefields? Are they all equal in value? If so, you can assume that the other side will distribute 1/3 of troop total to each front. If not, you can use that to your advantage, if you know in advantage what the values are.
but you still need to know more rules of the game to win it.
The strategic value of each battlefield is the same. Win any two and the war is won. You have already sent your troops. The other side uses no system of placing troops. Basically they are just as likely to send all of their troops to 1 battle field as they are to send 1/3 of their army to each battlefield. The question is asking you to evaluate how effective a 1/4:1/4:1/2 strategy is when your opponent uses no logical strategy. A tougher question could be, find the most effective strategy.

10. My brain tells me there is a way to solve this. Checking back when I figure it out!

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