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  1. Yesterday
  2. Playing baseball

    Am I understanding your claim correctly? Are you stating that it is impossible for a ball to give the appearance to a bystander of traveling straight up and down over the course of 8 seconds?
  3. Last week
  4. Drop two sticks

    Simulation shows the probability to be 0.75. This corresponds to 100% intersection if the needles align with opposite diagonals and 50% if the align with the same diagonal. Here is a figure that suggests how this comes about: We chose here a needle length of about 1.26. A simple construction shows (light red) the area where a needle of that length could land and (dark red) the region that its center point can occupy. The center point of a green needle landed on the green dot. The green bow-tie is the region the needle can occupy with its center fixed at the dot. The blue dot is a reflection in the diagonal, and the blue bow tie is the region the mirror image of the green needle can occupy. Note the coincidence of the lower left boundaries of the bow-ties. As the green needle moves through its allowable positions in a CW motion, the blue needle does the same in a CCW motion. During exactly 1/2 of that motion the two needles intersect. During the other 1/2 they do not. This is only a suggestive proof. The bow-ties can take different locations for different landing points. In some cases the blue and green needles never intersect, in others they always intersect and in still others they intersect for fractions of their motion that differ from 1/2. All the cases average out to 1/2.
  5. The lion and the tamer

    Greetings, Prof. T. Great to hear from you. The lion does start from the center, sadly for the tamer. The prevailing thought is for the lion to maintain the tamer's azimuth (his radius is shorter) and inch his way outward. By maintaining his azimuth, never leading nor lagging, the lion does not permit the tamer to gain advantage by reversing his direction. Although, since he can do so instantaneously, neither would the tamer lose advantage.
  6. Playing baseball

    First thoughts:
  7. Playing baseball

    A baseball player hit a ball high into the air. It took a perfectly linear path and came straight back down through the point where the man made contact after 8 seconds. Of course the ball only appeared to travel Linearly to us bystanders. Since the earth was spinning throughout the 8 second flight of the ball, describe the true flight the ball took during this period assuming earth's core is (0,0,0), make any other assumptions you need except leave the height of the ball unknown.
  8. cryptographer 1-6

    And how to decrypt this cryptographer 6?
  9. logic sequences

    Sure, they're all number! Lol
  10. HEY ROOK,

    help me with any viable answers for the similarity between the numbers 85, 17, 19, 4 and 2?

  11. logic sequences

    hello memebers , can anyone help me identify the similarity between the numbers, 85, 17, 19, 4 and 2?
  12. The 44th Riddle

    Assuming that a tie is not ratified, the first elder can suggest the allotment as: 9-0-1-1-1, knowing that the second eldest one will never accept the allotment as once the first one is dismissed he is going to get the biggest share, but remaining bankers will accept the allotment knowing that 1 is the maximum share they are going to get. Youngest is always going to decline the share for maximum share but if he is smart he would know the moment the sharing goes to the second eldest he would go to cut him loose. But if the 4 bankers vote down the first, the second eldest can suggest either of the three allotments: 10-1-1-0 or 10-0-1-1 or 10-1-0-1, all the bankers know that if they vote down this banker, the voting would come to third, third knows whatever he does the voting would go for a tie dismissing him, the forth knows that the sharing is the maximum he/she gets as if allotment comes to him he would not get anything
  13. Star Lord

    Glad you liked it, you are welcome!
  14. Star Lord

    The solution given on your website is fascinating. I learned something basic about spheres today! Thanks!
  15. Star Lord

    Yes, I expect my 2 Policeman strategy to fail. For example, suppose they landed on a spherical Earth. StarLord could start by walking around a circle enclosing 1/2 sq mile, then walk to another quadrant (while P2 is hurrying to get to SL's latitude). Once SL is trapped in that quadrant, walking one inch from the equator and Prime Meridian (thereby giving up a little less than 1/2 square mile), SL can capture slightly more than the quarter in total. i'm floundering with finding a 2 P strategy: The 1 P strategy is applicable and effective as soon as the game begins, so SL has no time to grab something outside the trap, but my 2 P strategy takes time before the quadrant can be nailed down.
  16. Earlier
  17. Is it possible to give what we don't have?

    The man didn't give sorrow. He gave sorrowfully. Does that give you Any ideas ;). Well those still probably didn't come From me. Perhaps I gave inspiration though, but that is something I have too. Which is a concept applying to all emotions.
  18. Crocodile Sophism

    1. The mother has to guess. Restating what the crocodile's riddleis saying something the mother knows. She knows that if she's right in her guess the child is returned and if she is wrong the child is eaten. 2. The mother has to guess Correctly. Any guess will not suffice for the child's return. 3. If she guesses correctly that the child will be eaten, then the child must be eaten. Next (after the eating (assuming she was right)) the child will be returned.... Crocodile poop. Otherwise, she was incorrect and the child will be eaten with no return (crocodile poop). 4. If she guesses correctly that the child will be returned, then the child will be returned unharmed. If she is wrong the child will be eaten and will not be returned (as poop). 5. A smart*** could guess something the crocodile will do to the child that is neither eating or releasing. For instance the mother does not know but could guess (either correctly or incorrectly) that the crocodile will touch, change, smell, hear, taste,the child. If she is correct then that is what the crocodilewill do: example, touch the child and letchild go. 6. Removing the option #5 the best option is to hope that whatever mercy provoked the crocodile to pose a chance forthe mother and child is the same mercy which would provoke it to relese the child. So guess that the child will not be eaten. Otherwise the best you get is crocodile poop.
  19. 3 remarkable numbers

    It can be argued that 2, 3, 5, and 7 are members of the sequence. Where the decimal expansion of n is 1, k = 1, and thus the number remains simply the prime. The integer sequence A097227 should, with the exclusion of these terms, state that the there are a minimum of two digits in each term, i.e., k > 1. Though the OEIS tries to be thoroughly correct, it is not always.
  20. Star Lord

    CaptainEd, your solution for 1 policeman is 100% correct. For two policemen I am not sure this strategy would work though.My solution is a bit different, following similar type of reasoning.
  21. The 44th Riddle

    After getting the answer it seems a tie is not ratified. Defrak was really close to the answer but he made a small error... 4 bankers: 9-0-2-1 (since 3 is needed for a majority) Therefore 5 bankers will be: 9-0-1-0-2
  22. The 44th Riddle

    I tried this two answers, but it's not working, i think that if there are 2 bankers left, whatever the solution, the younger will not accept, so he will take all the ingots. So the fourth one has to accept everything to not to remain two.
  23. The 44th Riddle

    Hi this is how i think about this problem. There are 2 possible assumptions. A tie is ratified (1) or a tie is not ratified (2). Starting with 2 bankers left, (1) 12-0 and (2) 0-12. 3 bankers: (1) 11-0-1, (2) 11-1-0. The banker receiving 1 will accept because when he doesnt he will receive nothing. 4 bankers: (1) 11-0-1-0, (2) 11-0-0-1 5 bankers: (1) 10-0-1-0-1, (2) 10-0-1-1-0
  24. Drop two sticks

    It turns out to rational. When the two sticks lie close to the opposite diagonals they always intersect, when they're near the same diagonal they intersect with a very simple probability that I think can be proved geometrically
  25. The 44th Riddle

    Thank you for your answers, i tried 6 0 1 3 2 and 7 0 1 3 1 , but it doesn't seem to work :'(
  26. The lion and the tamer

    Good thinking. Let's add the condition that the lion and tamer are point objects. Can they coincide? Also, could the lion reduce the radius of his circle to that of the lion and maintain any angular separation he might at some point have obtained? (Your solution prohibits this, but suppose the lion made one misstep and just for a moment he lagged the angle of the tamer.) This question has an amusing answer.
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