Maths puzzle -- What is the missing digit?

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In summary: The only proble is that he didn't calculate enough of them. The will close on the Golden Ratio - a significant clue to how the sequence can be generated.In summary, in order to find the missing digit in the given sequence, the clues provided suggest using an exponential sequence. The ratios between consecutive elements should approach the Golden Ratio, and the sequence should be similar to the Fibonacci series. Calculating ratios and differences between successive numbers can help in identifying the pattern.
  • #1
engnrshyckh
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Its a puzzle i can not able to solve it
In the fig attached we have to find what will be the digit in the missing box i can't figure it out
 

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  • #2
@engnrshyckh:

I will give you these clues:
1) The pyramid shape is irrelevant. The sequence 2, 3, 6, 8, 15, 22, 38, x, 98, 156 is sufficient.
2) If the terms are labelled ##A_0=2##, ##A_1=3##, ##A_2=6##, etc; then the even A's are computed with a slightly different formula than the odd A's.
3) ##A_{-1}## is not zero.
 
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  • #3
@engnrshyckh: Let me know if you've cracked it or need more assistance.
 
  • #4
.Scott said:
@engnrshyckh:

I will give you these clues:
1) The pyramid shape is irrelevant. The sequence 2, 3, 6, 8, 15, 22, 38, x, 98, 156 is sufficient.
2) If the terms are labelled ##A_0=2##, ##A_1=3##, ##A_2=6##, etc; then the even A's are computed with a slightly different formula than the odd A's.
3) ##A_{-1}## is not zero.
Still i am not sure how to solve it. Is it some kind of arithmetic sequence or geometric sequence?
 
  • #5
You can calculate the differences between two subsequent numbers and check if these are somehow linked to other elements in the sequence.
 
  • #6
.Scott said:
2) If the terms are labelled A0=2, A1=3, A2=6, etc; then the even A's are computed with a slightly different formula than the odd A's.
While i did use this initially to find the solution, you can also give a single equation valid for both even and odd A's. (and no [itex] (-1)^n [/itex] or anything like that in it)
 
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  • #7
willem2 said:
While i did use this initially to find the solution, you can also give a single equation valid for both even and odd A's. (and no [itex] (-1)^n [/itex] or anything like that in it)
Using ##(-1)^n## obviously works. I also think there is a way to use absolute value. But for the purpose of providing a clue, those aren't very useful.To @engnrshyckh:
Here are a couple of additional clues:
4) One way of identifying a sequence that grows exponentially is to list the ratios between consecutive elements. If you do this with the Fibonacci sequence, you will see that the ratio approaches 1.618034, the Golden Ratio, ##\frac{1+\sqrt{5}}{2}##. If your sequence also closes on a ratio, then it is also exponential. However, note that, although the Fibonacci series is exponential, no exponential function is used to compute its elements.
5) After the 156, the next 10 numbers in the sequence are: 255, 410, 666, 1075, 1742, 2816, 4559, 7374, 11934, and 19307.

If you solve it, let us know. If you don't, show the results you got by applying the exponential test I described above.
 
  • #8
.Scott said:
Using ##(-1)^n## obviously works. I also think there is a way to use absolute value. But for the purpose of providing a clue, those aren't very useful.
I said i was not using that.
You can however get an exact formula for the n-th element of the series, and it does involve (-1)^n.
If you type [insert recurrence relation here], a(0)=2, a(1)=3, a(2) = 6 in wolfram alpha, you'll get the exact solution.
.Scott said:
However, note that, although the Fibonacci series is exponential, no exponential function is used to compute its elements.
There is an exact non-recursive formula for the elements of the Fibonacci series, which does use the exponential function.
 
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  • #9
willem2 said:
If you type [insert recurrence relation here], a(0)=2, a(1)=3, a(2) = 6 in wolfram alpha, you'll get the exact solution.
I see. You go back one more term to get the even/odd information.
The absolute value method that I had in mind actually generated the sequence -2, 3, -6, 8, -15, 22, ...
Then you needed to take the absolute value of those terms to get the target sequence.

I like your method better.
 
  • #10
mfb said:
You can calculate the differences between two subsequent numbers and check if these are somehow linked to other elements in the sequence.
Clever. I missed that
 
  • #11
willem2 said:
While i did use this initially to find the solution, you can also give a single equation valid for both even and odd A's. (and no [itex] (-1)^n [/itex] or anything like that in it)
These are successive ratio 1.5,2,1.333,1. 875 but these are not the same as in geometric propagation.
 
  • #12
engnrshyckh said:
These are successive ratio 1.5,2,1.333,1. 875 but these are not the same as in geometric propagation.
Why are you calculating ratios?

mfb said:
You can calculate the differences between two subsequent numbers and check if these are somehow linked to other elements in the sequence.
 
  • #13
DrClaude said:
Why are you calculating ratios?
Difference is not the same also 1,3,2,7,7... To use arithmetic propagation farmula
 
  • #14
engnrshyckh said:
Difference is not the same also 1,3,2,7,7... To use arithmetic propagation farmula

Here's a clue: it's not a Fibonacci sequence!
 
  • #15
... but it's quite close. Might be interesting to calculate the difference in each case...?
 
  • #16
PeroK said:
Here's a clue: it's not a Fibonacci sequence!
118 is the correct ans thanks for the help
 
  • #17
engnrshyckh said:
118 is the correct ans thanks for the help
If i am not wrong
Screenshot_20200403_173700_com.android.chrome.jpg
 
  • #18
engnrshyckh said:
118 is the correct ans thanks for the help
It can't be ##118##. That's too big.
 
  • #19
engnrshyckh said:
These are successive ratio 1.5,2,1.333,1. 875 but these are not the same as in geometric propagation.
OK. But I gave you several more numbers in the sequence. Calculate all of the ratios for pairs up to 19307/11934. What you will discover is that it IS an exponential sequence - very similar to Fibonacci.
 
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  • #20
PeroK said:
It can't be ##118##. That's too big.
Then what i am missing?
 
  • #21
DrClaude said:
Why are you calculating ratios?
He's calculating ratios because it is a possible method for detecting an exponential sequence (suggested by me). The only proble is that he didn't calculate enough of them. The will close on the Golden Ratio - a significant clue to how the sequence can be generated.
 
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  • #22
engnrshyckh said:
Then what i am missing?
How does 118 work out? I don't see the pattern.
 
  • #23
.Scott said:
OK. But I gave you several more numbers in the sequence. Calculate all of the ratios for pairs up to 19307/11934. What you will discover is that it IS an exponential sequence - very similar to Fibonacci.
Yes its an exponential sequence but i am unable to find its equation which gives the correct answer
 
  • #24
.Scott said:
He's calculating ratios because it is a possible method for detecting an exponential sequence (suggested by me). The only proble is that he didn't calculate enough of them. The will close on the Golden Ratio - a significant clue to how the sequence can be generated.
I have something a lot simpler! Are there two answers?
 
  • #25
It is not 118.
Clue #6: The portion of the sequence that we are working with is monotonically increasing. So it is between 38 and 98.
 
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  • #26
PeroK said:
How does 118 work out? I don't see the pattern.
I used method of difference see the picture
 

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  • #27
engnrshyckh said:
Yes its an exponential sequence but i am unable to find its equation which gives the correct answer
It's not just an exponential equation. The ratio is the about the same as for the Fibonacci Series. So you should ask - how does the formula for generating the next Fibonacci number (##v_i = v_{i-1} + v_{i-2}##) result in the Golden Ratio?
 
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  • #28
.Scott said:
It's not just an exponential equation. The ratio is the about the same as for the Fibonacci Series. So you should ask - how does the formula for generating the next Fibonacci number (##v_i = v_{i-1} + v_{i-2}##) result in the Golden Ratio?
Enlighten me i shall be greatfull
 
  • #29
One last clue:

## 2 + 3 \approx 6##
##3 + 6 \approx 8##
##6 + 8 \approx 15##
 
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  • #30
We're not suppose to just give you the solution. So here's another (hopefully final) clue:

We know (2, 3, 6, 8, 15, ...) isn't Fibonacci because:
6 <> 2+3 (just misses)
8 <> 3+6 (just misses)
15 <> 6+8 (just misses)
22 <>
 
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  • #31
PeroK said:
One last clue:

## 2 + 3 \approx 6##
##3 + 6 \approx 8##
##6 + 8 \approx 15##
I stopped typing my clue in as soon as I saw yours pop up.
Clearly, we are on the same page!
 
  • #32
.Scott said:
We're not suppose to just give you the solution. So here's another (hopefully final) clue:

We know (2, 3, 6, 8, 15, ...) isn't Fibonacci because:
6 <> 2+3 (just misses)
8 <> 3+6 (just misses)
15 <> 6+8 (just misses)
22 <>
Thanks got it in some terms we add and aubtract 1 alternatively 👍
 
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  • #33
willem2 said:
You can however get an exact formula for the n-th element of the series, and it does involve (-1)^n.
If you type [insert recurrence relation here], a(0)=2, a(1)=3, a(2) = 6 in wolfram alpha, you'll get the exact solution.
And now that a solution is finally revealed, @willem2 solved it with this:
## v_i = 2v_{i-2}+v_{i-3} ##
 
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  • #34
.Scott said:
And now that a solution is finally revealed, @willem2 solved it with this:
## v_i = 2v_{i-2}+v_{i-3} ##
It is also easy to show that both approaches are the same. Take
$$
v_i = v_{i-1} + v_{i-2} + (-1)^i
$$
and replace ##v_{i-1}## on the rhs using the same recurrence relation.
 
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  • #35
The "absolute value" method I referred to was this:
## v_i = v_{i-2} - v_{i-1} +1 ##
can generate this sequence:
2, -3, 6, -8, 15, -22, ...

The absolute value of each element in that sequence gives you the sequence we were working with.

Oh yes. Someone should say it: 59.
 
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<h2>1. What is a "Maths puzzle"?</h2><p>A "Maths puzzle" is a type of problem or game that requires the use of mathematical concepts and skills to find a solution.</p><h2>2. What is a "missing digit"?</h2><p>A "missing digit" refers to a number or digit that is not given in the puzzle and must be determined by using the information provided.</p><h2>3. How do I solve a "Maths puzzle -- What is the missing digit?"</h2><p>To solve this type of puzzle, you will need to carefully analyze the given information and use mathematical operations and logic to determine the missing digit.</p><h2>4. Are there any tips or tricks for solving these types of puzzles?</h2><p>Some tips for solving "Maths puzzle -- What is the missing digit?" include trying different approaches or strategies, breaking down the problem into smaller parts, and checking your work for errors.</p><h2>5. Are there any real-life applications for solving "Maths puzzle -- What is the missing digit?"</h2><p>Yes, the skills used in solving these types of puzzles, such as critical thinking, problem-solving, and mathematical reasoning, are applicable in many real-life situations, such as budgeting, planning, and decision-making.</p>

1. What is a "Maths puzzle"?

A "Maths puzzle" is a type of problem or game that requires the use of mathematical concepts and skills to find a solution.

2. What is a "missing digit"?

A "missing digit" refers to a number or digit that is not given in the puzzle and must be determined by using the information provided.

3. How do I solve a "Maths puzzle -- What is the missing digit?"

To solve this type of puzzle, you will need to carefully analyze the given information and use mathematical operations and logic to determine the missing digit.

4. Are there any tips or tricks for solving these types of puzzles?

Some tips for solving "Maths puzzle -- What is the missing digit?" include trying different approaches or strategies, breaking down the problem into smaller parts, and checking your work for errors.

5. Are there any real-life applications for solving "Maths puzzle -- What is the missing digit?"

Yes, the skills used in solving these types of puzzles, such as critical thinking, problem-solving, and mathematical reasoning, are applicable in many real-life situations, such as budgeting, planning, and decision-making.

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