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  2. Hana

    Turn the paper upside down then add.
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  4. @Plasmid I translated your notation into mine, as far as we are gone, we have same results (excepted some doublets). I thought about interpolation, too, but I did not go this way estimating there is not enough data.
  5. I also come up with there not being a solution, although admittedly with a bit of hand waving toward the end. Without a computer (or at least not much): Edit: SMH I just realized that the stipulation of i being in the range from 1 to 2j doesn't hold for all cases (specifically I listed examples of i=3, j=1 that I overlooked) so I would need to rethink if there are more possibilities, or trudge through everything by hand.
  6. I heard this one a long time ago...and it probably would help to have said they were stranded on an island for a long time...but given that: Or some variation on that...
  7. I have invented a new puzzle called QUODRIX QUODRIX_T.pdf
  8. I have invented a new puzzle called KARAKIRI KARAKIRI_T.pdf
  9. What if I ask A if they feel bad when they lie?...if they can't answer (because they never lie) then they must be the truth teller. If they answer yes or no then ask B the same question... again if they can't answer they are the truth teller... If they answer yes or no then C is the truth teller... SO NOW ASK THE TRUTH TELLER IF (A) IS THE LIER...HIS ANSWER SHOULD SOLVE THE ISSUE !!!
  10. Same as rocdocmac Combinatorics:
  11. (See **/ALL CAPS added to the quoted section.) So the first part of this is correct, and I'm convinced this is the only way to determine who's who, but you only have about a 17-22% chance of asking the Random (or Variable) Answerer AND getting the answers you need from that person. (Not sure I have the percentages right, but it's that ballpark.) When I'm presented with a logic puzzle, I've always assumed it could be solved, but I think maybe this one has an additional layer: You have to determine whether there is a way to solve it A. everytime; B. just sometimes or C. never. This puzzle falls under B (I'm pretty sure). So it is a good epistemological lesson: 1. It is possible to determine truth, but 2. it is sometimes by chance and 3. you can increase your odds of getting to the truth by asking the right questions, but 4. sometimes we don't (or can't) have enough information to determine something with certainty. Unfortunately, #4 is often overlooked, even in the field of science.
  12. 3x=30 => x=10 y+10+10=25 => y=5 z+5+5=17 => z=7 (7*2)+5*(2*10)=114
  13. 3 pairs of tiles. Each pair identical, 3 pairs different. Keeping the 3x2 layout shown, assuming the tile positions can be individually swapped and individually turned by 180 degrees, how many combinations are there? Extention: How many combinations if there were 6 unique tiles?
  14. without waiting to hear your answer, I think the answer is
  15. Check the video I prepared with a beutiful riddle and detailed solution https://www.youtube.com/watch?v=-wVfA2LhwZk&ab_channel=Math%2CPhysics%2CEngineering
  16. Thanks for finding the problem. I was so sure that if X contradicts Y, they must be in different categories - it did not occur to me that can be both liars.
  17. Giving it a shot at writing with different notation
  18. I have written a program that emulates the manner in which I manually solve these puzzles. The program works - but only most of the time (regardless of the size of the puzzle). Since there are some puzzles that I cannot solve, I have come up with the following 'reasons': There is some solving process that I have not yet discovered There is a bug in some of the puzzles making them not solvable. There was one puzzle, I believe Hard 283, that I was able to solve, but solving it took a fair amount of effort writing notes, etc - it was not fun. This makes me suspect that I am missing a solving process... Anyway, if you are an 'expert' at this game, or know someone who is, I would welcome the opportunity to communicate with you. Thanks.
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