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  1. Last week
  2. Previously, Maiden’s boat could change its heading instantaneously. Ogre’s heading could change only by virtue of following a circular path along the shore at his current speed. His rotational speed was thus far from infinite, and perhaps that disadvantage was unfair. So in this final puzzle iteration we’ll limit the boat’s linear speed to be f times that of Ogre, as before, but now we’ll also limit the boat’s angular speed to be never greater than g times Ogre’s top angular speed. A moment’s thought tells us that unless g is greater than unity the boat’s best strategy is to run at full speed from the center to the shore, keeping its initial bearing, no matter where on the shore Ogre initially stands. That is, never to turn the boat. That sucks for Maiden (e.g., she loses if Ogre initially stands at the boat's initial heading) and it sucks as a puzzle. So we’ll say the boat can change heading faster than Ogre can. For clarity we’ll set g = 2. We’ll implement that limit by giving the boat’s motor three discrete settings that can be switched instantly an unlimited number of times: clockwise (CW), full speed ahead (FSA), and counterclockwise (CCW.) In the two turning modes the boat turns but maintains its position; in FSA mode it moves forward but does not turn. Boat’s path is thus a succession of arbitrarily short line segments joined at angles of Maiden's choosing, with the time cost of the angle depending on its size. If the boat starts in the middle of the lake, how large must f now be for Maiden to escape? Edit: Extra credit (tough): If Ogre's top speed is 1 lake-radius per minute, and Maiden chooses the boat's initial heading at the center, what's her shortest time safely to shore?
  3. Tharagorn


    A type of sardine eaten by flounder?
  4. Earlier
  5. I tried entering a number on a whim to see what would happen. It seems to have taken it. Is it normal to get an error message if you type the wrong answer?
  6. Hi guys, I would greatly appreciate the solution to this... For some context and familiarity, the puzzles are usually pattern spotting based and continuing it. Also, I must add that I've gathered an 'obvious' solution to this that seems to fit in but is not the correct answer, that being '2332' (according to the rules of entering the answer). http://peconinja.web.fc2.com/777e/CDE.html or
  7. 1minute 10 seconds. You toast two pieces of bread at once the first time (30 seconds) When they are both toasted on one side, take one of the pieces off (5 seconds) and put the untoasted piece of bread on the grill (5 seconds). Wait 30 seconds for the last piece to toast. The riddle doesn’t say that you have to toast both sides of the bread. Instead of taking out both pieces the second time, you can unplug your grill (assuming the grill is electric). Arguably, the shortest amount of time is 1 minute 13 seconds. You would use the added 3 seconds to flip the piece of bread that stays on the grill and make sure that it doesn’t burn.
  8. three slices of bread are to be toasted under a grill. the grill can hold two slices at once but only one side is toasted at a time. it takes 30 seconds to toast one side of a piece of bread, 5 seconds to put a piece in or take a piece out and 3 seconds to turn a piece over. what is the shortest time in which the three slices can be toasted?
  10. Yes it is possible. The Triborough Bridge in New York connects Manhattan, the Bronx and' Queens.
  11. Hmmm. I hadn't considered that. Is there a different solution if the murderer did not own the murder weapon?
  12. Nicely done. As for adding some wrinkle to the problem, how about this? Suppose we have to add some time for her to get out of the boat before she starts to run. We could say the ogre must have an angular separation of s radians from the boat when it lands, and then minimize f. Hmmm. I'm guessing the same path just minimizes f to a slightly larger value. Hi @The Lonewolf Brand and welcome to the Den. That would mean the maiden's boat and the ogre have the same speed. She can escape from a faster ogre.
  13. But unless the problem has been edited, it is stated: "along with the fatal gun that belonged to one of them ... the murderer." But not absolutely necessary for the solve.
  14. Interesting idea. How would we pose that question exactly? .
  15. I'd say that the minimum value of f is slightly less than... I'll play around with it a bit to see how much I can lower it. Another interesting addition might be, once the minimum f is found, to find the minimum travel distance (e.g., amount of gas) needed for some f a little higher than the minimum.
  16. Jaxon

    The Murderer

    If you SAY anything, truth or lie, you'll die. In order to stay alive is to say nothing
  17. What a deliciously challenging and intriguing puzzle.
  18. If you think you've heard this one before, read it carefully. It's not the standard puzzle. A beautiful maiden sits in a boat at the center of circular lake. On shore waits an ogre anxious to have his way with her. Being an excellent sprinter she knows she can outrun and therefore escape the lumbering ogre if only she can land her boat safely. But should the ogre reach her landing point first, alas, all will be lost. The boat is propelled by a motor capable of only a fraction f of the ogre's speed. What is the minimum value of f that will permit the Maiden to escape?
  19. An archaeological artifact is depicting figures of some natural and artificial objects like the sun, moon, comet, star, flower, horse, bird , insect, headdress, mountains, river, house, weapons, bonfire and necklace. The translation of the symbol message below is "WIND, RAIN, FLAME, SOIL, ESSENCE". According to experts, there are 5 polyomino tiles that were used as patterns for making the outline of the figures in this artwork. They also believed that these 5 tiles altogether should fill and fit in any of the 16 figures depicted above. What are these polyominoes?
  20. Vdsffbfdfgxgbbbhdfgnfdgnfdbgtd fgffgbfbgfgdfgbgfbgffbfghbfgngfgnhgfgnfff hhfghhngfggfbdfgbggfnhffffffffffssssfefggfgffd
  21. Phil1882 is right ... there is a discrepancy. The 6th term may possibly be 532 901 * 532 901 + 1 = 283 982 410 001.
  22. That's some two-year-old. And yes, it's time to ..
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