# Tag Info

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In the first column all numbers are multiples of 5. In the last column all numbers are multiples of 7. By addition and subtraction we obtain (63 + 70 + 56) - (60 + 55 + 65) = 3^2. In the second column and the fifth column, all numbers are multiples of 10 plus one prime. By addition and subtraction we obtain (800 + 80 + 200 + 40 +3) - (160 + 13 + 400 + 20 + ...

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The missing number is The reason is that

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We start from the top. The sum of the first row is 315 + 165 + 145 +83 = 704. The sum of the second row is 133 + 13 + 3 + 1 = 150. The sum of the third row is 113 + 19 + 31 + 50 = 213. The sum of the fourth row is 12 + 2 + 32 = 46. If we subtract from the sum of the first row the sum of the other three rows, we have 704 - (150 + 213 + 46) = 295, so the ...

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The answer is most likely If we look at the numbers in the 1st triangle The 2nd triangle Lastly the 3rd triangle(equivalent to 2nd triangle)

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Could it be Reason

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Here is the python solution for the same problem. I am not posting the optimized version of the same code as this is more structured and easy to follow with the question statements. # S does not know the answer # S knows that P has no unique product, remove them s = {} p = {} for y in range(3, 97): for x in range(2, min(y, 100-y)): if p.get(x*y, ...

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I think answer is : Reasoning :

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Answer for a,b,c and d are : Reasoning

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The answer to the puzzle is: Puzzle 1: Puzzle 2: Puzzle 3: Putting it all together:

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So we can break up the solution as which decodes as Although I suspect there may be another level of decoding and the final answer should be

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On the bounty challenge: Here is a secret bounty recipe that uses one operation and 74 ingredients. How I got this solution: Also, 　 On the general question: Here is a secret recipe with 61 57 ingredients.

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Perhaps the answer is Because And the fact that We can deduce the answer: Which matches Hint 6 in that (Those not after "-" is the original text):

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This type of puzzle is an exercise in mind reading. All 4 answers have roughly equally valid logic supporting them, so you have to "read the mind" of the person posing the question to get the "correct" answer. Other answers have explained why 3 of the 4 choices are logical solutions. The remaining puzzle is therefore to find a similarly convincing ...

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Partial Answer 1. 2. 3. So overall I think

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I know this is answered and ticked, but:

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First, the easy deductions: Next, And now repeat: A new deduction can be done here: And now the rest falls by process of elimination:

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The final grid: Step by step solution (I’ll clean up if needed in the morning): 1: 2: 3: 4: 5: 6:

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First we construct a square A,C,G,F then we draw the bisector BE of the sides AC and FG. We set A=3, C=7, F=5, G=2. Then we set B=1, E=4, and on the middle of the bisector we put the D=6. All rows and columns add to 11.

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The same 56 solutions but with logical reasoning instead of bruteforcing:

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There are 56 solutions: I wrote an algorithm to find these solutions.

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Sum: is Method:

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Methodology:

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I believe the answer is Reason

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We know that: It then follows that So the question boils down to finding The solutions are therefore:

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This is not a full answer, but it looks like you're getting quite desperate for some response to this, so I'll write up the thoughts I've had so far, in the hope that either someone can take it and continue to get the full answer, or at least that you will see which parts are clear to potential solvers and which parts may still need hints. Basically we're ...

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The missing numbers are Reasoning So

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First of all, let's see why your brute-forcing fails. (This is the puzzle part, the rest is plain old math.) No matter which you chose, the number at the bottom right would have to be both odd and even at the same time, so there's no integer solution. However, there are four equations and four unknowns, so we should have at least one solution (unless the ...

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2648: 1942: 2899: 2869: 1278:

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Well, judging from the hint, each $[m\ast n]$ means In our case, we seem to have only $[n\ast n]$, in which case So rewriting all the expressions we've been given: Word 1 (2 letters): $[3*3]+[1*1]+[2*2]+[2*2]$ Word 2 (5 letters): $((-[1*1] + [3*3] + [4*4] + [8*8] + [27*27]) \cdot [2*2] + [1*1] + [1*1] + [5*5] \cdot [27*27]) \cdot [2*2]$ Word 3 (2 ...

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The answer is most likely Because

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Overall solution The nine symbols are, in the arrangement given: Step-by-step deductions From the factorial relationship, But from the perfect-power relationship, So The top left (division) relationship From the square root relationship, Going back to the perfect-power relationship, Now for the big product relationship: From the division ...

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