My guess would be 2581 = 2
I won’t explain how I came to that yet, just in case it is right!
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This teaser had me going round in circles until Don gave a hint!
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Well, it is right. Well done Bobby.
I thought it might make a change from the A-Level maths puzzles of late …
… and before one of my next ones that I thought was nigh on impossible 
No doubt you agree with Bobby. Well done.
I think it would now be safe to provide the explanation.
I must admit that I only really looked at it properly after your hint, after which it jumped out at me.
The number on the right of the equals sign represents the sum of enclosed areas in the previous number. For example, the number 8 has two enclosed areas (2 circles, more or less), whereas the number 7, say, has no enclosed areas. So the number 7778 would equal 2, whereas 8887 would equal 6.
I’m sure there are more eloquent ways to express that!
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I don’t think so ! As thebadyogi said, “brilliant”.
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Not from me, my solution is full of holes.
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I found this next one ‘difficult’.
In other words, I couldn’t solve it myself. I even found it took a bit of effort to convince myself that the given answer is correct - well done Excel !
The sum of the cubes of 1 and 2 (ie 1 + 8) equals 9
Simply identify two other positive numbers whose cubes add up to 9.
PS. Both these numbers can be expressed as vulgar fractions, and their summed cubes, really are exactly 9.
PPS. I’m told that the originator of this puzzle (it’s just maths) came up with the solution c.1900 ie before computers, using only pencil and paper !!
I found that quite astonishing and to share that astonishment is the real reason for posting this one
I may be being a bit dim here, but for example 3 cubed plus -2.62074139421 cubed equals 9, as does 4 cubed plus -3.80295246076 cubed etc etc. I acknowledge there has been some rounding here, which may preclude these answers.
Or did you mean to exclude negative numbers?
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I haven’t solved it yet but I think the fractions should each be in the form a/b where a and b are integers. Otherwise there is an infinite number of irrational solutions.
I don’t know about negatives though. One for Don to clarify.
Yes, that’s what’s I was alluding to. I expect your theory is correct regarding a/b.
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Luckily for us you want a total of 9. If you had specified a total of 1 we would still be struggling for the next 300 years.
I did intend to exclude negative numbers. Thank you Steve.
I should have written
The sum of the cubes of 1 and 2 (ie 1 + 8) equals 9
Simply identify two other positive numbers whose cubes add up to 9.
I will modify the initial post. Many thanks
Don
That is the basis of the solution that I have.
I found a solution that included a negative fraction.
I will have another look for just positives
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hi Steve. ‘Rounding’ is not permitted
It has to be perfect !
Now, having said ‘perfect’ … I believe the numbers I have, deliver a perfect 9.
Each numerator and each denominator has 12 digits. Both numbers are in the form a/b (where a and b are integers, as noted by Ravvie). The denominator is the same in each number and the numerators are both larger than the denominator.
A careful check with Excel shows no sign of anything other than Zeros after the decimal point in 9.000… but Excel only runs to 30 decimal places
I suppose that I should really check the arithmetic manually, but …
12 digit numbers probably exclude a brute force approach. I could only test all possibilities up to 10k in Excel. It is probably beyond Python too.
My answer if allowing negative numbers is much more down to Earth:
20/7 and -17/7
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Just to keep things in context … the guy who provided the numbers that I have, did it just after the year 1900, using pencil and paper …