20

I think the next element is Because


18

First take the capital cities of the countries in order Now notice that So the next country he would have to visit would have to have


13

The answer is The individual answers, starting from top left and moving right, are Then use A-Z = 0-25.


10

We need this (modulo any careless mistakes I've made): Explanation:


10

Note 1: Number 3 was solved by hagfy in the comments. Note 2: Where two or more digits are equal in any ordering below, the digits are sorted numerically. 1. 2. 3. 4. 5.


8

This appears to be Specifically: Then, So: [Also, a minor inconsistency:]


7

The answer maybe: The reason is:


6

First, let's divide the $5$ cells like this: If you observe the colored cells (the non-black cells) upside-down: The next thing is that, the $5$ cells are actually representing the binary. With black cell denoting $0$ and colored cells denoting $1$. (This refers to hint 2b.) But, it's not a regular binary. It's: So, if we evaluate the numbers: Yep, you ...


6

A lower bound for the number of moves is because This can be done as follows:


6

I think the length of the longest such sequence is Proof of upper bound Proof of lower bound How did I find such a sequence As Florian F has pointed out in the comments there is a simpler integer choice. Given that And pushing this Fibonacci link a bit further we know that


5

The answer is Because


5

Just a visual cue of Gareth's answer


5

I would say that the Because,


5

COMPLETE SOLUTION: Answers provided for all 12 clues, including 4 found by @Randal'Thor... These give us the letters: This letter sequence: Translated, this reveals:


5

Partial answer: The second series fits the function g(x) = (29*x^7 - 694*x^6 + 6560*x^5 - 31150*x^4 + 77711*x^3 - 94876*x^2 + 46740*x + 46080)/720 When you insert the values 0 - 7 for x, then the values of the series are emitted in ascending order, but you write, that the order may be other than given. When inserting the value 8, then the result is 546, ...


5

We need for the following reason:


4

Solving the number puzzles: See Jens's answer - I didn't manage to get this one. See Jens's answer - I didn't manage to get this one. Turning the numbers into letters: The final step, motivated by the appearance of is to yielding the solution.


4

The rule is: Question 1: Question 2: Question 3:


4

Progress? Solver eyl327’s visual approach is reminiscent of a picture from another puzzle, leading to this worksheet and a couple others, not necessarily mistake-free, ... ... where S, R and L are interpreted as ... ... like turtle graphics. Overwriting has obscured some information in the worksheet above but the resulting form is suggestive in ...


4



3

Partial answer for the clues: I wonder if this might be something to do with Partially filled grid:


3

Perhaps the sequence goes like this being I confess that I don't know Further remarks:


3

Partial Answer: I'm not getting far with this. But i think it could be: This is probably nonesense but I think I can see: Below are my "workings". I fear I am also barking up the wrong tree, especially since I cant see any further patterns... So basically my answer was almost a complete guess :)


3

One answer could be As, For,


3

I think(partial):


3

The answer might be this: Considering that the picture can be of any scale in all diagrams i.e. : each cross (axes) may have different scales as scales or markings are not mentioned.


3

I think the answer is Reasoning


3

The next number is Why:


3

The answer is Reason:


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