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List the expressionist numbers (Posted on 2016-05-30) Difficulty: 4 of 5
Consider numbers like 343 or 2592.
343=(3+4)^3
2592=2^5*9^2.

We have just shown that some numbers stay unchanged when a number of mathematical operators are added /inserted, without changing the order of the digits.
Within our puzzle lets call those numbers expressionist numbers.
Let us limit the set of acceptable mathematical symbols to the following operators: +, -, *, /, ^, sqrt, !. and any amount of brackets.

My questions:
In the period between 10 A.D. & 2016 A.D. what years were labeled by expressionist numbers?
How many such years will there be between 2017 A.D. & 9999 A.D.?

Bonus: How about one, two (or more) 5-digit examples?

No Solution Yet Submitted by Ady TZIDON    
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Comments: ( Back to comment list | You must be logged in to post comments.)
re: Computer solutions | Comment 6 of 10 |
(In reply to Computer "solution" part 1 -- no guarantee of completeness by Charlie)

In addition to the limitations previously mentioned about no more that two square roots in a row and precision limitations, etc. there's also the fact that I didn't allow for starting any formula with a leading negative sign, so that for example 9-1 could be written as -1 + 9 (not that these satisfy what the puzzle asks for; it's only an example).
  Posted by Charlie on 2016-05-31 07:39:57

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