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More ways to get Braingle...

If There's a Camel

Logic puzzles require you to think. You will have to be logical in your reasoning.

 

Puzzle ID:#10515
Fun:*** (2.5)
Difficulty:*** (2.92)
Category:Logic
Submitted By:griphookph***!!!

 

 

 



Every year during his birthday, the Sultan sponsors 3 camel races with the following prizes (listed in order 1st, 2nd, 3rd):

RACE A
$500
300
100

RACE B
$250
150
75

RACE C
$150
100
50

$500 bonus for winning all 3 Races. (SLAM)
$200 bonus for winning 1st, 2nd, and 3rd in any one Race (SWEEP).

ALI BOBO tells you that he owns the 3rd ("Aluminum"), 6th("Boron"), and 9th("Copper") fastest camels. He concedes that KAREEM owns the 1st, 4th, and 7th fastest camels, while SHARIF has the 2nd, 5th, and 8th fastest entries. There are other owners but with far inferior camels.

The Rules

a. Maximum 3 camels per owner.
b. A camel can run only in one race.
c. An owner may enter his camels all in one race or distribute them as he desires.

Last year ALI BOBO's camels won third place in each of the 3 Races. His gross winnings amounted to $225.

ALI BOBO wants a risk-free strategy to increase his total winnings.

QUESTION: What should be ALI BOBO's strategy?





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Comments

gooblah
Feb 25, 2003

It is totally dependant on what the other racers do and we don't know what they WILL do until we see the answer. It's based purely on assumption, which to me, isn't logical.
dewtell*us
Feb 27, 2003

Ali's strategy is not entirely risk-free.
If the #5, 7, and 8 camels enter race A,
1 and 2 enter race B, and 4 enters race C,
then Ali scores 0 + 75 + 100 = 175, which
is less than last year. If the other two
players are colluding against Ali to minimize
his results, it's worth it to them to
sacrifice one place in race C in order
to knock him out of third place in race A.

griphookph*
Feb 27, 2003

Thanks. I think in Dewtell's scenario Ali will get 0 + 75 + !50 ( 225). Whatever the opponents strategy may be Ali Bobo's winnings will be more unless there's collusion. In that case, Ali Bobo gets the same $225. The strategy of the others will not lessen Ali's winnings. Only their own.
tangerine**
Feb 27, 2003

I thought it had a great idea behind it, but it was based on assumption as someone said previously ... still nice one to think about n.n; ... how long did that take you? x.x;
-tangerine-
griphookph*
Feb 28, 2003

Thanks Tangerine. No, the teaser is not based on any assumption. Whatever happens or whatever the other owners do, the stategy will work. Thanks
dewtell*us
Mar 10, 2003

No, in the scenario I posted, Ali should
only get $100 for race C - he has the #6
camel racing against #4 (and a field of
slower camels), so he should get second
place, which you said was worth $100.
Were you assuming that he would pick up
the third prize too in this scenario?

Admittedly, the other two owners don't
really gain by doing this, because some
other owner picks up the extra $50 that
they squeeze out of Ali's share. But perhaps
they could collude with the guy who owns the #10
camel to split up that $50 third place prize
in race C at Ali's expense.
griphookph*
Mar 13, 2003

You are absolutely right, it is not 100% risk free. That scenario is possible if the other two know how Ali would field his camels and Ali cannot react. As you also correctly pointed out, the others have nothing to gain. Thanks,
Christina0213
Mar 30, 2003

That was fun!
fatcranium
Apr 29, 2003

I agree that the posted "solution" does not meet the criteria of being risk-free, since there is a possible scenario where Ali would end up with only $175. Any other attempts by Ali to alter his strategy from the previous year have also have minimum payouts less than $225. The only truly risk-free thing for Ali to do would be to repeat his previous strategy. In that case, the minimum payout is $225 and any strategy changes by his opponents will result in a higher payout.



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