shakespeare sonnets

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normy

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there are a total of 154 sonnets. if we choose number 86 and add that same number, but reversed, we find 86 plus 68 results in 154.

question is this, is there some formulae by which the above may be reproduced for any given number.?
 
normy said:
there are a total of 154 sonnets. if we choose number 86 and add that same number, but reversed, we find 86 plus 68 results in 154.

question is this, is there some formulae by which the above may be reproduced for any given number.?
Click to expand...
If you are dealing with 3-digit numbers, only numbers:

  • less than 198 and

  • more than 22 and

  • integer multiple of 11

can be treated this way (note that 154 is more than 22 and less than 198 and multiple of 11)
 
same rules as stated by SK (198 and 22 included)

hundreds digit + unit digit = tens digit
 
Last edited:
a huge thanks to SK and Skeeter, what a speedy response.

does this mean that for 154, only 86 will work? in other words are 86 and 68 the only pair which
gives same result?

thanks again guys.
 
normy said:
a huge thanks to SK and Skeeter, what a speedy response.

does this mean that for 154, only 86 will work? in other words are 86 and 68 the only pair which
gives same result?

thanks again guys.
Click to expand...
After looking at the responses,

What have you tried?​

Please share your efforts - not in words but mathematical steps.

Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:


Please share your work/thoughts about this problem.
 
[imath](10x+y)+(10y+x) = 11(x+y) = 154 \implies x+y = 14[/imath]

95+59, 86+68, 77+77
 
thanks again you guys, i am somewhat blown away.

my best wishes to all.
 
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