*DI Marathon for CAT 2007*

[maxximus]

Originally Posted by warrior

solve this

a corporate business man has two cubes on his office desk. every day he arranges both cubes so that the front faces show the current day of the month. what numbers are on the faces of the cubes to allow this?
Note: You can't represent the day "7" with a single cube with a side that says 7 on it. You have to use both cubes all the time. So the 7th day would be "07".

we have 12 faces. so v can 12 nos.

we require exactly 12 nos. to represent 30 days of a month.

0-9 - ten digits. but we require two 1s to represent 11th day and two 2s to represent 22nd day...

so the digits shud be 3,4,5,6,7,8,9 -one each

1,2 - two each

another observation: two 1s and two 2s shud be in 2 different cubes.

regards

[maxximus]

Originally Posted by warrior

this also

you're a cyborg in a pistol duel with two other cyborgs. you have been programmed to fire pistols with an accuracy of 33%. the other two cyborgs shoot with accuracies of 100% and 50%, respectively. the rules of the duel are one shot per-cyborg per-round. the shooting order is from worst shooter to best shooter. thus, you go first, the 50% guy goes second, and the 100% guy goes third; repeat. if a cyborg dies, we just skip his or her turn, obviously. what should you shoot at in round 1 to maximize your chances of survival over time?

hi...after lotsa deliberation...its a better bet to hit the 100% guy...the solution is really cumbersome n requires a lot of xplanation...will put it briefly here...

choose 100% guy.

i hit :

1/2 (i hit 100)x 1/4 (75 doesnt hit) x 1/2 (i hit 75) = 1/16

=> 1/16 + 1/16 x 1/4 (75 doesnt hit in round 2) x 1/2 (i hit in round 3).........

a g.p with r = 1/8, a = 1/16, sum = 1/14.

i dont hit 100, 75 hits 100 in 1st round:

1/2(i dont hit 100) x 1/2(75 chooses 100) x 3/4 (75 hits 100) x 1/2 (i hit 75) = 3/32 + ...a gp with r = 1/8, sum = 3/28

i dont hit, 75 doesnt hit 100 in 1st round:

1/2 x 1(75 chooses either of us) x 1/4 (75 doesnt hit) x 1/2 (100 chooses 75) x 1 (100 hits 75) x 1/2 (i hit 100) x 1/4 (75 misses me) x 1/2(i hit 75) +... a gp with r = 1/8

sum = 1/192

total probability of my survival = 1/14 + 3/28 + 1/192 = 41/192 = .183


choose 75:


75 hits 100 in 1st round:


1/2 (i miss 75) x 1/2 (75 chooses 100) x 3/4 (75 hits 100 ) x 1/2 (i hit 75) +...a gp with r =1/8...

sum = 3/28



75 doesnt hit 100 in 1st round:


1/2 (i miss 75) x 1 (75 chooses either of us) x 1/4 (75 misses 100 ) x 1/2 (100 chooses 75) x 1 (100 hits 75) x 1 x 1/2 (i hit 75) +...a gp with r =1/8...

sum = 1/28


total prob of my survival = 3/28 + 1/28 = 1/7 = .143

so, hitting 100 is a better bet...if am not missing any case...which i dont think i am

warrior bhai...please let me know


regards

[chop suey]

Originally Posted by warrior

solve this

a corporate business man has two cubes on his office desk. every day he arranges both cubes so that the front faces show the current day of the month. what numbers are on the faces of the cubes to allow this?
Note: You can't represent the day "7" with a single cube with a side that says 7 on it. You have to use both cubes all the time. So the 7th day would be "07".

1st cube has numbers 0,1,2,3,4,5 n 2nd has 0,1,2,6,7,8...now for 9 one could turn 6 upside down and get 9 ....is the solution correct

[krsh.vik]

Originally Posted by warrior

this also

you're a cyborg in a pistol duel with two other cyborgs. you have been programmed to fire pistols with an accuracy of 33%. the other two cyborgs shoot with accuracies of 100% and 50%, respectively. the rules of the duel are one shot per-cyborg per-round. the shooting order is from worst shooter to best shooter. thus, you go first, the 50% guy goes second, and the 100% guy goes third; repeat. if a cyborg dies, we just skip his or her turn, obviously. what should you shoot at in round 1 to maximize your chances of survival over time?

Haven't done any mathematical calcln .... I think it should be 100%

[veritas]

i think on 1 cube v can have 0 1 2 3 4 5 and on the other cube v can have 0 1 2 6 7 8 and 9 can be displayed by reversing 6

[warrior]

Originally Posted by chop suey

1st cube has numbers 0,1,2,3,4,5 n 2nd has 0,1,2,6,7,8...now for 9 one could turn 6 upside down and get 9 ....is the solution correct

correct boss

[doomsayer]

Originally Posted by warrior

this also

you're a cyborg in a pistol duel with two other cyborgs. you have been programmed to fire pistols with an accuracy of 33%. the other two cyborgs shoot with accuracies of 100% and 50%, respectively. the rules of the duel are one shot per-cyborg per-round. the shooting order is from worst shooter to best shooter. thus, you go first, the 50% guy goes second, and the 100% guy goes third; repeat. if a cyborg dies, we just skip his or her turn, obviously. what should you shoot at in round 1 to maximize your chances of survival over time?

definitely at 100% guy.
Suppose if i hit 50%guy and if he dies , the next chance is 100% guy's and he definitely kills me.

@maxximus what r u using 75 here? there is only 3 persons with accuracy 33,50,100

[gaya3_b]

Good work guys!!!!!!!!

[unstoppablemuks]

Originally Posted by warrior

this also

you're a cyborg in a pistol duel with two other cyborgs. you have been programmed to fire pistols with an accuracy of 33%. the other two cyborgs shoot with accuracies of 100% and 50%, respectively. the rules of the duel are one shot per-cyborg per-round. the shooting order is from worst shooter to best shooter. thus, you go first, the 50% guy goes second, and the 100% guy goes third; repeat. if a cyborg dies, we just skip his or her turn, obviously. what should you shoot at in round 1 to maximize your chances of survival over time?

does it really requires a calculation ? its very logical that if i want to live and killing others in the only option for that, i will eliminate that option thru which chances of getting killed are higher. so obviously i will kill that 100% fellow first

[MG_1806]

Originally Posted by maxximus

0-9 - ten digits. but we require two 1s to represent 11th day and two 2s to represent 22nd day...

so the digits shud be 3,4,5,6,7,8,9 -one each

1,2 - two each

another observation: two 1s and two 2s shud be in 2 different cubes.

regards

You need to check it again mate.What happens if 0 and 3 are on the same cube and you wants show 30