BrainDen.com - Brain Teasers

# bonanova

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1. ## Can you spell Alex?

UR - me. Martini - nice going. Cold one on me at Morty's tonight.

4. ## Alex's birthday cards

For the fun of it I marked two quarters with 3 black sides and looked at 50 cases. 10 blacks -> 7 black on other side 10 blacks -> 10 black on other side 10 blacks -> 6 black on other side 10 blacks -> 6 black on other side 10 blacks -> 5 black on other side ======================== 50 blacks -> 34 black on other side => 68%
5. ## Tennis tournament

What if there were two contestants?
6. ## How do you make it?

Amends ... have one on me. http://tbn0.google.com/images?q=tbn:AeD0ew...egalbeermug.jpg
7. ## How do you make it?

I'll see your Newton's Third Law and raise you a Solar Powered Truck! Gas ........? What gas? Good one.
8. ## How do you make it?

I'd love to hear your solution. But consider this, regarding mine.

10. ## Alex's mug challenge - no math needed

Further clarification. This differs a little from the OP for clarity - it does not change the solution. Jamie is blindfolded. The four mugs are placed on the corners, randomly up or down. Each move, Jamie touches only two mugs [not all of them]. Here is what constitutes one move: Davey turns the lazy susan an arbitrary multiple of 90 degrees. Touching only the lazy susan, Jamie chooses any two adjacent corners or any two diagonally opposite corners. He picks up those two mugs. He puts them back on the same corners, individually flipped or unflipped, i.e. individually up or down, as he chooses. Jamie gets 5 moves. At the end of any move: if the mugs on the lazy susan are all up or all down, Alex rings the bell and Jamie wins.
11. ## Alex's mug challenge - no math needed

Clarifying. Jamie is blindfolded. The mugs are placed on the four corners, randomly up or down. Move #1 - Jamie knows where the four corners of the lazy susan are and can pick up [1] two adjacent mugs - or - [2] two diagonal mugs Then he can feel whether they are up or down. He can flip either, neither, or both and replace them. Davey randomly turns the lazy susan to a new position. Jamie doesn't know what Davey did. Move #2 - Jamie [still blindfolded] does the same thing again. Davey turns the lazy susan again. Move #3 ... same. Move #4 ... same. Move #5 ... same. At this point [or before] all the mugs must be up or all must be down. At any time, if all the mugs are up or all the mugs are down, Alex rings the bell, and Jamie wins. Can Jamie ensure a win - without relying on luck?

Two caveats:
13. ## Alex's birthday cards

If you reason that because the only cards that can show a B face [the BB and BW cards] are drawn with equal likelihood the answer must be 50%, then try the experiment. Do precisely what Alex did, ignoring the WW card for simplicity. Make two cards: BB and BW. Place one from your pocket onto a table. [1] If it shows B, add 1 to your possible outcomes total. [2] If the reverse side is B, add 1 to your favorable outcomes total. Repeat until you have 30 possible outcomes. Now, are the favorables closer to 15? or to 20? If it's 17 or 18, do another 30. And maybe another 30. 1/2 or 2/3 will eventually come into sharp focus. And when it does, keep in mind that you drew the BB card 1/2 of the time! If I were a betting man, and I'm not, I'd bet an entire donut on 2/3. Why? Because of the equal likelihood requirement. You see a B face 100% of the time when the BB card is drawn but only 50% of the time the BW card is drawn. 2 cards x 2 faces = 4 equally likely events. 3 events show a B face. 2 events are favorable. Basically, you count the BB card twice - because it can show a B face two ways; and count the BW card once - it can show a B face only one way. Does that make sense?

15. ## Boil this egg for exactly 3 minutes

You want to boil a perfect 3-minute egg. For a timer, you have only two 4-minute fuses, that do not burn at an even rate. Can you have breakfast without a runny [or overly hard] egg?
16. ## Some simple physics

No. And I hope he brought a parachute.
17. ## Alex's birthday cards

You make a valid point. I hope that doesn't sound condescending ... The answer depends on the premises of the set-up. The way you describe the set-up I agree the answer is 1/2. But look back at the story. I created a narrative that presupposed nothing except that a card was placed on the table. And then it was observed that the top face was black. It wasn't presupposed to be black. And if it doesn't matter which color it would have been, a card needn't even be drawn; only to ask the question: if I pull a card at random from my pocket and place it on the table ... what are the odds that the other side will match? Where the answer is clearly 2/3. Presupposing the color that's visible [as in your analysis] makes the answer 1/2. Part of the fun I get in constructing these stories is providing enough clues for an unambiguous answer. Sometimes I succeed , Sometimes I get it wrong.
18. ## Alex's 55-pint Birthday Bonanza

Get Alex, Jamie and Davie to remove 2 or 3 glasses at a time, keeping things balanced at each step.
19. ## Alex's 55-pint Birthday Bonanza

Happy Birthday to me ... HBTM ... etc sang Alex as he strolled into Morty's last night and then announced, Boys, I've got a real treat for ya tonight! First, take a look at this. And he hung from the ceiling a complicated, interconnected set of five scales, whose 10 balance pans he'd labeled A, B, C, ... H, I, J. Now the barkeep gave me one request, bein' it's my birthday on Saturday, and all. He's gonna draw out fifty-five cold pints. Then, if we can place a different number of pints into each of these balance pans, we'll have a real party, cuz the drinks will be on the house! Every pan gets a pint to start with, and all five scales have to balance. Alright boys, let's get at it ... we have until midnight to get this done. Otherwise we pay for the drinks. Feel free to help Alex, Jamie, Davey and the boys celebrate! Edit for clarity The marks on the bars are equally spaced.
20. ## Alex's birthday cards

Intuitive probability fails when it compares favorable to possible outcomes that are not equally likely. I buy a lottery ticket. There are two outcomes - it's a winning ticket or it's not. One outcome is favorable. My odds of winning the lottery are 1/2. Ooops ... reality check! The times that this is really fun is when the faulty result is feasible. With the black and white card problem, you can easily make the cards and do the experiment say 30 times. A valid intuitive solution notes that 1/3 of the cards have opposite color on the other side. The probability of opposite color is 1/3 and same color [black or white doesn't matter] is 2/3.
21. ## Alex's birthday cards

I think you're considering each side as a separate entity ... That's it, exactly.

kewl.
23. ## God 'vs' the rock

If you're referring to the God I know, the answer is this. God cannot fail.
24. ## Alex's birthday cards

What if it was side 2 that was black?

It can't be.
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