- The number on their head is always higher than zero

- One of the numbers is the total of the other two numbers.

If they can guess their numbers, they are free to go.

- Person 1 gets asked if he knows his number. He says he doesn't.

- Person 2 gets asked the same, but also replies that he doesn't know

- Person 3 is being asked but doesn't know either.

Since none of them answered wrong. They get another chance.

- Person 1 again doesn't know.

- Person 2 also doesn't know.

- Person 3 however does know the answer this time: It's 148 on his head. This answer is correct and he is allowed to leave.

Question: What are the numbers on the heads of person 1 and 2 and how does person 3 know his own number?

]]>This is an easy one... how many can get it first time?

]]>Extention: How many combinations if there were 6 unique tiles?

]]>https://www.youtube.com/watch?v=-wVfA2LhwZk&ab_channel=Math%2CPhysics%2CEngineering

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[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 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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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.

]]>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).

]]>Engineers are confronted with two apparently true but contradictory statements:

a) To fly, lift must equal the weight of the airplane (Lift = Weight).

b) Commercial airliners such as Boeing 747-400 and Airbus 320 have thrust-to-weight ratios of about 0.3. i.e. Thrust / Weight = 0.3

If the engine thrust (Thrust) is 3N, then the weight must be 10 N, and the Lift must be 10 N as well.

But there is a significant problem: According to this logic, 10 N of Lift is 7 N greater than the 3 N of Thrust. This is impossible as 3 N of Thrust cannot produce the Lift of 10 N.

Hence a paradox arises, as equations (a) and (b) appear true when stated individually. But combined they produce equation (c) ‘Thrust / Lift = 0.3’ that is false (i.e. impossible).

Therefore, one of the equations (a) or (b) must also be false. But which one?

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There is a troupe of five mummers: a drummer, a dancing bear, a piper, a juggler, and a jester. One always tells the truth, one always tells lies, and the remaining three tell a mixture of truth and lies. To find out who tells what, the following clues are presented:

Drummer: I always tell a mixture of truth and lies.

Juggler: That is not true.

Jester: If the bear is always truthful, the juggler tells nothing but lies.

Bear: That is false.

Piper: The drummer always tells the truth.

Jester: The piper tells nothing but lies.

Can you figure out who tells what based on this information, and how?

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.. ... . ..... ... . ... . ... ..... . .. . ..... ... ... (I=J)

The only clues were:

"It's a cipher. You'll tap into it soon enough"

Surely it's something to do with morse code?

Can someone please help me to understand?

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I'm having problems on calculating the volume of this solid (see image bellow).

Thank you in advance!

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From what’s left, she gives 1/5 + 10 to Carol.

Then she gives 1/2 of what’s left +10 to Nancy.

She keeps 5.

How many buttons did she start with ?

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