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without waiting to hear your answer, I think the answer is

Silverware...knives forks and spoons.

Check the video I prepared with a beutiful riddle and detailed solution https://www.youtube.com/watch?v=-wVfA2LhwZk&ab_channel=Math%2CPhysics%2CEngineering

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.

Giving it a shot at writing with different notation

Comment on your answer

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.

Do not worry, on my first attempt, I did not manage it to write it clearly enough that I myself could read and understand it. When you asked your question, I checked my solution written about a year ago and wondered whether it would not be easier to start from the beginning. I have rewritten it and found a kind of notation: P.S. Can someone change in the title ONE in ONCE? Thanks in advance.

Having to actually write it out in such a way that others can read and follow it does wonders for imposing clarity...

Bonus question: Answer your question. Why don't you post your solution?

I think I've got a solution, but not everyone ends up being restricted to one exact age. Does that mean I messed up somewhere?

On an island, every statement is true if the islander is aged less than L and false if he is at least L years old. Find their ages. [1] A: "B is more than 20 years old." [2] B: "C is more than 18 years old." [3] C: "D is less than 22 years old." [4] D: "E is not 17 years old." [5] E: "A is more than 21 years old." [6] A: "D is more than 16 years old." [7] B: "E is less than 20 years old." [8] C: "A is 19 years old." [9] D: "B is 20 years old." [A] E: "C is less than 18 years old."

There be sixty-and-four flowers-de-luce (in a grid 8x8), and the riddle is to show how I may remove six of these so that there may yet be an even number of the flowers in every row and every column. I am not able to remove 6 of them: interactive version What am I missing? Solution. that does not help me. I got it now, to late to delete.

I don't see anything barring use of other numbers in exponents. Nothing explicitly says you can only use 7s. It's certainly implied that the 3 7s are the central parts so you can't do something like add or subtract a different number but you can square or cube. Closest I can get with the more limited interpretation: 7!/sqrt(7!)÷7=10.14 Looser interpretation: (7!)^(1/5)+(7!)^(1/5)-7^0=10.003

Rats, I was going to say that ( Sqrt(7!) - 7^0 ) / 7 is close enough that no one's likely to notice the difference.

Using the number 0 or extra 2's does not fit the allowed operations. Only Sqrt(4) + 4 + 4 = 10 seems allowable.

You want to satisfy 7 7 7 = 10 You can add, subtract, multiply and divide, use parentheses, square root, exponent and factorial. So, for example: 2^2 + 2^2 +2 = 10 Sqrt(4) + 4 + 4 = 10 8 + 8^0 + 8^0 = 10 You are also not allowed to manipulate the right side of the equation (e.g. 7^0 * 7^0 * 7^0 = 10^0).

I did some research... At first, the drawing Nick made is somewhat confusing. What he calls "forward force" should be "thrust" and what he calls "thrust" should be "drag". Just google "drag thrust weight lift". If thrust=drag and lift=weight, the plane will fly at constant speed at constant height (plenty of pages). Now, the question is how much thrust we need to generate lift=weight (or a little better). On the end of the article https://en.wikipedia.org/wiki/Lift-to-drag_ratio, there is a table: latest air-crafts have a coefficient over 19.

I agree with harey. As was said earlier, you can rule out the Drummer from being the Truth teller because he said he tells truth and lies, and you can rule out the Piper as being the Truth teller because he says someone else always tells the truth and there's only one Truth teller. So there are three possible Truth tellers. (1) If the Jester is the Truth teller then the Piper must be the Liar, as Babysnoot said, but that's not enough to rule out other possible truth tellers. (2) If the Juggler is the Truth teller then you know the Drummer must be the Liar. Since the Drummer can't be the Truth teller, and the Truth teller said his statement that he tells both truths and lies is false, the only thing the Drummer could be is the Liar. This kind of works against Babysnoot's argument. (3) If the Bear is the Truth teller, then we know the Juggler isn't the Liar but I can't narrow it down more than that. I also considered the possibility that the statement that the other three "tell a mixture of truth and lies" means that there must be both some true statements and some false statements among the three, but that still doesn't help. If the Drummer and Juggler are mixes then the Drummer's statement is True and the Juggler's statement is False, so any solution excluding them as Truth teller and Liar would work. And for the Drummer = Liar / Juggler = Truth teller scenario, you would have the Jester's first statement be True and the Piper's statement be False, so that doesn't rule anything out.

I fear there are multiple solutions. Babysnoot is correct, just the only reason to proclaim Jester truthteller is that there is no further contradiction in the system. For Bear=truthteller, Drummer=liar, others=mix (it does not matter whether what they say is true or false), there is no contradiction in the system, neither. Does someone agree?

I'm not sure I agree with harey. While it's true that if a plane's power is lost it will drop more slowly than a ballistic due to the drag of air against the wings keeping it from accelerating too quickly, while it's flying straight and level and the net vertical velocity is zero I would imagine that it shouldn't have an impact. I'm also puzzled by the fact that a plane can stay aloft when the force of gravity is greater than the thrust of the engine. It probably has something to do with the fact that a plane can only stay aloft when the airflow across its wings is laminar, and that if the airflow becomes turbulent (for example if the pilot pulls the nose up too much and the plane goes into a stall) then it can no longer maintain enough lift and starts falling. But I don't know how to account for that with equations and account for balancing out the force of gravity.