### Brain Teasers

# If There's a Camel

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?

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?

### Hint

Sometimes we must sacrifice some battles to win the war.### Answer

Ali Bobo must enter Copper in Race A, Aluminum in Race B, and Boron in Race C.SCENARIOS

1. Kareem defends his Slam and fields his camels in RACES A,B, and C according to their speed. Shariff follows that same strategy.

ALI's Aluminum will win in Race B over the K(4th) and S(5th). Boron will win in Race C over K(7th) and S(8th). Copper will still place 3rd in Race A. Total Winnings $500.

2. Kareem defends his SLAM. Shariff follows Ali's strategy.

Aluminum will place second to S(2nd) in Race B. Boron will place second to S(5th) in Race C. Copper will place third to K(1st) and S(8th). Total winnings: $350.

3. Kareem loses his mind and does not go for the grand slam. He enters his 3 camels in Race A. Shariff follows his strategy in Scenario 1.

Copper will not win anything in Race A. Aluminum will win in Race B. Boron will win in Race C. Winnings: $400.

4. Same as Scenario 3 but Shariff has same strategy as Ali.

Copper loses in Race A. Aluminum places second in Race B. Boron places second in Race C. Winnings $250.

5. Kareem camels all in Race A. Shariff's all in race B.

Copper loses in Race A. Aluminum still places second in Race B. Boron wins in Race C. Winnings $300.

6. Kareem defends his slam. Shariff camels all in race B.

Copper will place second in Race A. Aluminum will still be second in Race B. Boron will win over K(7th) Winnings:$600.

7. Kareem and Shariff has same strategy as Ali.

Copper will be third, Aluminum will be third. Boron will be third. Winnings:$225. Same as last year.

There are other scenarios but with the strategy with the worst case scenario for Ali is $225.

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## Comments

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.

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.

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.

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.

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-

-tangerine-

Thanks Tangerine. No, the teaser is not based on any assumption. Whatever happens or whatever the other owners do, the stategy will work. Thanks

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.

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.

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,

That was fun!

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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