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What would be your answer to the question mark? The most common answers are 40 and 96... Does anyone could say why? Hence if it is given the first terms in a sequence and the sequence is not well defined, the next term is able has multiple right solutions, even infinite solutions. For instance, in the next problem Find the solution which I gave one solution, is able to have infinite answers, even the other answers given in the problem can be right... Just only have to take polynomials with two variables x,y which satisfies the conditions, for example,can you find a polynomial with variables x, y satisfying the first conditions and such that f(13,4) = 123 or f(10,9) = 123?... So my conclusion is this one: Can you post one riddle where different right solutions are valid?and why my "riddle" is able to have 40 or 96 as valid solutions?can you find other right solution and say why?

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## Comments

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TopNewestI think they expect 96 as the answer if they do this. \(a+b=a×(b+1)\) But like @Nihar Mahajan said you can have \(\infty\) solutions

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The riddle has infinitely many solutions using LZOB or Lagrange interpolation, since the choices are not provided.

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Exactly, for the problem Find the solution you can use Lagrange interpolation with two variables, please wait a bit, and I'll give the answer

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please, be calm. I can not answer to everybody

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We have \( f(5,3) = 28, \space f(12,10) = 222 \space , f(9,1) = 810, \space f(4,2) = 26, \space f(8,3) = 511, f(10,1) = 911, \space f(7,3) = 410\). This problem using Lagrange interpolation is able to have \(\infty\) answers. For example, I want furthemore \(f(13,9) = 123.\) Is evrything allright so far? haha. Ok, I'm going to look for a polynomial with variables x,y and some constants a,b,c,d,e,f,g,h,i, ...fullfiling these conditions,(notice I'm going to repeat this factor (y -1) and (y - 3), I would not to do it, but I'm going to do it for clarity) so the polynomial has to be \(\small f(x,y) = a(x -5)(y -3)(x -12)(y -10)(x - 9)(y -1)(x - 4)(y -2)(x - 8)(y -3)(x - 10)(y -1)(x - 7)(y - 3) + \) \(\small + b(x -5)(y -3)(x -12)(y -10)(x - 9)(y -1)(x - 4)(y -2)(x - 8)(y -3)(x - 10)(y -1)(x - 13)(y -9) + \) \(\small + c(x -5)(y -3)(x -12)(y -10)(x - 9)(y -1)(x - 4)(y -2)(x - 8)(y -3)(x - 7)(y - 3)(x -13)(y - 9) +\) \(\small + d(x -5)(y -3)(x -12)(y -10)(x - 9)(y -1)(x - 4)(y -2)(x - 10)(y -1)(x - 7)(y - 3)(x - 13)(y - 9) +... \) and get the constants a,b ,c ,d e,f, g, h,... fulfilling the requisites... so this problem has \(\infty\) right solutions... Ok, now I'm going to eat... Later I'll review the comments

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How is the answer 96 or 40?

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I got 96 but not 40.

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please, be calm. I can not answer to everybody

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Why are you assuming the function is a polynomial? (just asking)

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Its not wrong to assume a polynomial right?

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@Deeparaj Bhat. And it was a comment and not a question

Hey I was askingLog in to reply

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52

Assuming there is something fundamental operation that isn't explicit, just like the assumption that the last answer is also added to the next equation... Goes like this... The pattern is multiplying the second number secretly by a sequential while number, just like secretly having the last answer added to the next equation...

1+(4[×1])=5 2+(5[×2])=12 3+(6[×3])=21 8+(11[×4])=52

This makes all the answers correct.

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## 1+(4[×1])=5

## 2+(5[×2])=12

## 3+(6[×3])=21

## 8+(11[×4])=5

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The answer is 40. :P

In this riddle the answer of the previous statement is added to the terms of the original statement.

First statement starts with 1 + 4 = \(\color{red}{\text{5}}\).

Second statement:- \(\color{red}{\text{5}}\) + 2 + 5 = \(\color {blue}{\text {12}}\).

Third statement:- \(\color{blue}{\text {12}}\) + 3 + 6 = \(\color{green}{\text {21}}\).

Fourth statement should be \(\color{green}{\text {21}}\) + 8 + 11 = \(\boxed{40}\).

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## 1+(4[×1])=5

## 2+(5[×2])=12

## 3+(6[×3])=21

8+(11[×4])=52Log in to reply

That was supposed to be a clarification of my own post... Sorry. 'Doing this from my phone while walking to the store.

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