Brainteaser Tuesday

1. 500

2. 8

How did you get 500?

it costs you 1250 bananas to bring 1750 bananas to the 250 mile mark.

it then costs you 750 bananas to bring 1000 bananas to the 500 mile mark.

use 500 bananas to bring the other 500 bananas to the finish line. Easy game

The other one was retarded unless I'm missing something.

Does the monkey need to eat bananas on the way back?

If the exact distance is 1000 miles and he has to eat 1 banana for every mile, then he will eat 1000 bananas for the duration of his trip. And if he can only carry 1000 bananas, then there you go - he can bring 1000 bananas and will have none by the end of the trip. Unless I'm missing something...

Here's one for the chubby kids:

What is the probability that in a given bag of M&Ms, all the M&Ms happen to be purple?

Here's another:

Is it more cost effective to kill a chicken for its meat or raise it for its eggs? Explain.

1. carry 1000 bananas to the 333 mile mark, leave them there and do it three times to accumulate 2001 bananas at the 333 mile mark. Then, carry 1000 bananas to the 833 mile mark, leave them there and do it again to accumulate 1000 bananas at the 833 mile mark. The other banana left at the 333 mark, you're gonna have to ditch. Then, carry the 1000 that you have the rest of the way to save 833 bananas. A similar question was given in the JSC interviews and i got it using this thought process. your goal is to make milestones to eliminate the number of trips u need between those milestones.

2. you and your wife each shook hands with 4 people. This, i had to draw out and dont really have an explanation for why. The only combination i found to work was when couple 1 greets 0 and 8 ppl each, couple 2 greets 1 and 7 ppl, couple 3 greets 2 and 6 ppl, couple 4 greets 3 and 5 ppl, and u and ur wife greet 4 and 4 ppl each.

heres mine: you have 13 bottles of wine, 1 of which u know is poisoned. you have to serve wine to your guests in 24 hours, but you have no idea which one is poisoned. You have 4 rats to test the wine on, but the effects only show 23 hours 59 minutes after consumption. What method would you use to determine the poisoned wine?

I buy 13 new bottles of wine, because I have money and am not willing to go to jail over a thousand dollars.

The answer to the banana question is 0.

The answer could be 0,1,2,3,4,5,6,7, or 8. The question doesnt supply enough information to determine otherwise.

Only knowing the effects after 23 hours and 59 minutes makes this question a bit trickier, but anyways:

Leave bottle 13 out. If all rats live you know it's bottle 13. If any rat dies you know it's not 13.

Bottle 1: give to rat #1 Bottle 2: give to rat #2 Bottle 3: give to rat #3 Bottle 4: give to rat #4 Bottle 5: give to rat #1 and 2 Bottle 6: give to rat #1 and 3 Bottle 7: give to rat #1 and 4 Bottle 8: give to rat #2 and 3 Bottle 9: give to rat #2 and 4 Bottle 10: give to rat #3 and #4 Bottle 11: give to rat #1,2,3 Bottle 12: give to rat #1,2,4

See which rat(s) are dead, if any, the poison could be in bottle 13.

the monkey can bank 2000 bananas..........he simply throws the bananas in front of him, one after another, every time he moves the entire banana mass a mile, he eats one, and hes left with 2000. If we say there is an energy cost to throwing we would have to discount those (problem does not specify). Since carrying one banana cost the same energy as carrying 1000, the throwing shouldn't be a problem.

For the wine/rat question am I right in thinking that you could actually test up to 16 wines if you wanted to?

Logic:

You need to identify a unique set of rats for each wine, so that there is a one-to-one mapping between poisoned wine and dead rats at the end. The number of unique rat sets (assuming you number the rats as above and so can tell the difference) is:

4C4+4C3+4C2+4C1+4C0

=1+4+6+4+1 =16

gobigorgohome's answer is completely correct, I'm just illustrating that he could have, for instance, also selected the set 1, 3 and 4- and there are 16 sets in total.

The chicken question is basically identical to a model of collusion in an oligopoly. The key factor, as stated, is how the present value of future eggs compares to the (present) value of chicken (though the chicken only has one value as it is consumed immediately). The expected present value depends on 3 things- the expected number of eggs that a chicken will lay in each future period, the value of an egg to you, and your discount factor

A further complication (as noted above) is that you don't have to eat the eggs that the chicken lays- you could let them grow into chickens, and then eat the meat. Once you assume this, it actually becomes quite a complex optimisation problem (since there are infinitely many paths you could take- you could hatch the egg, get more eggs from the chicken and then eat n eggs, or n-1 eggs, etc). The result will depend on how much you like eggs vs. chicken meat...

afroman23

MXC, you're correct, you can check up to 16 wine bottles. The way I solved it was by using binary numbers, with each rat being a significant digit. I guess it was more natural for me due to my engineering background.

I didn't account for the monkey having to eat on the way back as well... Same logic though, so in that case you would go 200 miles, drop 600 bananas and eat 200 on the way back, repeat, then on the third trip bring the rest so you accumulate 600 + 600 + 800 = 2000 bananas at the 200 mile mark. Then, you bring 1000 bananas to the 533 mile mark, drop 334 and eat 333 on the way back, then bring the other 1000 and accumulate 334 + 667 = 1001 bananas at the 533 mile mark. Go the rest of the way with 1000 bananas (ditch the 1 you can't carry) and monkey saves 533 bananas.

Since my wine one was solved, ill give another: you have 50 black marbles and 50 white marbles, and are given two empty jars. You are going to pour the marbles into the jars however you want ( you must use all of them) and then an executioner will blindfold you and present you with one of the jars at random. You will reach in and pick out at most one marble. If it is black, he will axe your head off right there. How do you minimize your chance of decapitation?

Part 2: He then changes his mind and says if you pick a white marble you will live. How do you maximize your chance of picking a white marble? In case you thought the answers were the same, theyre not.

good attempt, but unfortunately there is an underlying assumption that the distribution of the marbles within a jar are completely uniform once you pour it in. Like most brainteasers out there, the unspoken rule is no shenanigans.

I got 600 bananas

and 8 hand shakes

Anyone know any good brainteaser books?