1 
riddles / what am i / Mystery of a Sphere 
Feb 23^{rd}, 2024, 1:43pm 
Started by alien2  Last post by alien2 
A sphere inside a large circle; The beginning of triumph or defeat. At the end of borrowed time Twenty warriors will have wounded feet. Who/What am I? 
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2 
riddles / easy / Re: Geometric puzzle, two triangles 
Feb 18^{th}, 2024, 5:55am 
Started by rmsgrey  Last post by rmsgrey 
on Feb 17^{th}, 2024, 10:13am, Grimbal wrote:Now that I think of it, The blue triangle and the red triangle below are the same, just rotated 60°. Now the problem is that my first answer would imply an angle of 120° (1/3 of 360°). The second answer says it is 60°. So which one is it? And where did I go wrong? 
 This is the proof I came up with. The 60 degrees is the angle to the side of the intersection (the space you rotated the line through), which makes the angle above the intersection 18060=120. 
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4 
riddles / easy / Symbol 
Jan 25^{th}, 2024, 5:06am 
Started by alien2  Last post by alien2 
You wake up alone in a brightly illuminated white room, no clues whatsoever as to how you got there, except for a white oak flooring, with no windows, and one yellow door with no lock or doorknob. The milky white walls, that are out of the same material (and color) as the ceiling, feel like marble to the touch. You try to open the door, but to no avail. It is firmly closed. When you press a mysteriously phallic protuberance, one out of four altogether, which suddenly appear on one wall, popping one by one, a malted milk tablet materializes from the same wall, two meters away from where you’re standing, and falls on the floor, a meter from the wall, setting in motion a genuinely bizarre chain of events. You press the very same mysteriously phallic protuberance, just to be sure, and another malted milk tablet falls on the same spot on the floor. Well, now at least you know that you won't starve to death, since this room is similar to a holodeck, or a giant replicator. You’re not very hungry at the moment, which is perfectly understandable, to lose your appetite considering the circumstances, though you didn’t have your breakfast yet. So you decide to press another phallic protuberance, yet hardly at ease, neither w/o anxiety nor even w/o great fear. A toothbrush materializes, that is to say, it falls out of the wall on the other side of the room, so that the little hole or opening in the wall is only temporary and it lasts a few seconds. The toothbrush clatters to the floor. Well, it appears you won’t lose your teeth either, which can only be considered as good news. But you haven’t eaten yet, and you’re still anxious, trying not to panic, so you decide not to brush your teeth at the moment. It appears, we all have our bad habits. You decide to press the 3rd phallic protuberance. It is then when an ordinary broom is released from an adjacent wall. If anything, and if you agree that cleanliness is next to godliness, this room won’t be a mess. Lastly, you decide to press the 4th and final phallic protuberance. It is then when the door across opens pretty slowly, by making an eerie creaking sound. But it remains open for exactly three seconds before it closes abruptly and with a slam. You try several more times, by pressing the 4th phallic protuberance, apparently, the most important one, in order to try to escape the room, slowly starting to panic, running like a bat out of hell each time. But to no avail, since the door always closes in front of your nose, always lacking at least one more step. It is obvious that you are no Usain Bolt, unless, of course, you are, to whom this would be a piece of cake. But even if you were this sprinter, the cubic room would then be somewhat bigger and even you wouldn’t be able to leave the room by sprinting. You start to despair and slowly lose hope, occasionally comforting yourself with a malted milk tablet, since it is better to be angry, fretting etc. on a full stomach, and, of course, you need all the energy you can muster if you insist on trying to somehow leave this accursed room. Being an imprisoned man, you’re engaged in absurd and hilarious attempts to escape the gleaming room, and objects at your disposal, which can be replicated as many times as you wish (even though the room is hardly the Kalpavriksha, because of the stated parameters), might just be the keys to your escape. Yes, there is a way to escape. Happy puzzling! P.S. Inspired by the film “Symbol” (2009). 
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5 
riddles / easy / Re: The SpiderMan of Paris 
Jan 17^{th}, 2024, 7:54am 
Started by alien2  Last post by rmsgrey 
For the third variation, your expected return from taking 6 paintings is always the same, so, if you're just concerned with the monetary return, the only question is how riskaverse or riskseeking you are. If you're riskaverse, taking 3 of each type guarantees a 3painting payout; if you're riskseeking, taking 6 and 0 gives you either all or nothing. You can get more interesting by delving into utility curves  if, rather than 2 paintings being twice as valuable to you as 1, 3 paintings being triple, and so on, if you instead have some other relative values for different numbers of paintings, then that changes your expected value for various strategies. You have four options, each of which gives you a 50% chance of each of two possible outcomes  taking all the paintings from one set gives you 0 or 6; taking five from one and one from the other gives you 1 or 5; taking four and two gives you 2 or 4; and taking three of each gives you 3 or 3, which is just a guaranteed 3. Whichever pair gives you the highest total utility across the two possibilities would be your personal best pick. 
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7 
riddles / hard / Re: power of 3 close to power of 2 
Nov 13^{th}, 2023, 10:10am 
Started by jollytall  Last post by jollytall 
If I remember well, I proved few month ago that indeed this aL is the best sequence, but that was never validated by anyone. Nonetheless, I am more interested in the smallest absolute difference (i.e. not ratio) between 3^n and 2^m, where 2^m > 3^n. I came up with a related question to prove: 2^m  3^n > 2^(mn) if 2^m > 3^n > 3. With other words, if we write 3^n in base 2 then the first (i.e. highest value) n bits have at least one 0 among them. Yet with other words, we proved earlier that 3^n/2^m > 1e can be solved for any e, but even that solution is not that close, i.e. 3^n/2^m < 12^n 
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8 
riddles / what am i / Re: Diet? 
Nov 10^{th}, 2023, 6:51am 
Started by alien2  Last post by alien2 
Meh, the answer is probably silly (SPOILER): the positions of the big hand (the minute hand) and the small hand (the hour hand) at 6:00, 18:00, 12:00 and 24:00. 
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10 
riddles / hard / Re: Identify your favourite childhood games 
Jul 9^{th}, 2023, 8:42am 
Started by livinggod29  Last post by rmsgrey 
Here are my answers. Number 1, I'm not certain about, and 5 and 14 I have no idea on. 1 Blob Tag? 2 Musical Chairs 3 Hide and Seek 4 Hopscotch 5 6 Grandma's Footsteps 7 Simon Says 8 Marbles 9 Leapfrog 10 Sack Race 11 The Floor is Lava 12 Cops and Robbers 13 I Spy 14 15 Tug of War 
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