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## Question

I have a feeling this may give some people a challenge. Although there are always a few of you out there that seem to get these right away.

42, 40, 36, 39, 45, 46, 48, 52, 49, 54

What comes next in the sequence and why?

## 9 answers to this question

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I have a feeling this may give some people a challenge. Although there are always a few of you out there that seem to get these right away.

42, 40, 36, 39, 45, 46, 48, 52, 49, 54

What comes next in the sequence and why?

53. You take the original number, then subtract the difference between the 10's digit and the 1's digit.

42-(4-2)=40, 40-(4-0)=36, etc

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53. You take the original number, then subtract the difference between the 10's digit and the 1's digit.

42-(4-2)=40, 40-(4-0)=36, etc

That is the correct answer but quite not the correct solution. Our solutions are related but that's not the method I used.

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53. You take the original number, then subtract the difference between the 10's digit and the 1's digit.

42-(4-2)=40, 40-(4-0)=36, etc

Here is a three-digit example that uses my mathematical theory but would not work with yours:

156, 211, 200, 178, 255, 288, 354, 365, 387, 431 . . .

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I have a feeling this may give some people a challenge. Although there are always a few of you out there that seem to get these right away.

42, 40, 36, 39, 45, 46, 48, 52, 49, 54

What comes next in the sequence and why?

Prime numbers

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I have a feeling this may give some people a challenge. Although there are always a few of you out there that seem to get these right away.

42, 40, 36, 39, 45, 46, 48, 52, 49, 54

What comes next in the sequence and why?

Now I have tried the following method:

42, 40, 36, 39, 45, 46, 48, 52, 49, 54

Now reversing 42 ->24 ; 24-40=-16

40->04 ; 04-36=-32

36->63 ; 63-39=24

Likewise if i do for the other nos, I am getting multiples of 8.

I even obtained the same result (multiples of 8) while solving for the 3 digit sequence.

Am I proceeding in the right direction.If not provide a hint.

Edited by grey cells

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Now I have tried the following method:

42, 40, 36, 39, 45, 46, 48, 52, 49, 54

Now reversing 42 ->24 ; 24-40=-16

40->04 ; 04-36=-32

36->63 ; 63-39=24

Likewise if i do for the other nos, I am getting multiples of 8.

I even obtained the same result (multiples of 8) while solving for the 3 digit sequence.

Am I proceeding in the right direction.If not provide a hint.

The transposition of the number is correct but the subtraction from the following number is incorrect. It's interesting that it comes out to multiples of eight though. Perhaps someone will be able to explain that later as well.

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Thanks Alfred . I have been trying to get the answer for the Past 2 days. I am going to post the solution even if you have given it away.

original set: 42 40 36 39 45 46 48 52 49 54 53

transposed set: 24 04 63 93 54 64 84 25 94 45

Subtracting the transpositions from the nos. from the original set:

In the same order: 18 36 -27 -54 -9 -18 -36 27 -45 9

Now , divide the above numbers by 9 and subtract the result from the corresponding original nos.

Eg: 42-(18/9)=40

40-(36/9)=36

. .

. .

. .

. .

54-(9/9)=53

I did the subtraction correctly , But the idea of dividing with 9 did not strike me .I divided only with 2,3 and 4.The whole day today(well almost ) , my friend and I tried to solve this , even during the class hours.

GREAT puzzle , this.Please keep posting more such puzzles. :)And I want to add that this puzzle is a paradise for multiples.I tried adding instead of subtracting and I got .. guess what... a whole horde of multiples of 11!!!!

Edited by grey cells

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Thanks Alfred . I have been trying to get the answer for the Past 2 days. I am going to post the solution even if you have given it away.

original set: 42 40 36 39 45 46 48 52 49 54 53

transposed set: 24 04 63 93 54 64 84 25 94 45

Subtracting the transpositions from the nos. from the original set:

In the same order: 18 36 -27 -54 -9 -18 -36 27 -45 9

Now , divide the above numbers by 9 and subtract the result from the corresponding original nos.

Eg: 42-(18/9)=40

40-(36/9)=36

. .

. .

. .

. .

54-(9/9)=53

I did the subtraction correctly , But the idea of dividing with 9 did not strike me .I divided only with 2,3 and 4.The whole day today(well almost ) , my friend and I tried to solve this , even during the class hours.

GREAT puzzle , this.Please keep posting more such puzzles. :)And I want to add that this puzzle is a paradise for multiples.I tried adding instead of subtracting and I got .. guess what... a whole horde of multiples of 11!!!!

Nice work grey cells! I learned about the multiples of 9 trick as an accountant. If you ever have a difference when reconciling accounts you divide that difference by 9. If it's a multiple - chances are you have a transposition error somewhere in your work. Now as for why you were able to come up with multiples of eight when took the difference from the next number is another puzzle in itself. I'm going to check and see if it continues working for 7, 6, 5... as you progress.

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Thanks ALFRED for the information.Please do keep coming up with more such new ideas.

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