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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.)
Little start | Comment 1 of 10
After some try I've found little. Just one very smart under 2016
145=1!+4!+5!
Numbers higher than 2016 are not particularly smart
2520=(2+5)!/2+0
3125=(3*1+2)^5
4096=(4+(0*9))^6

Edited on May 30, 2016, 5:11 pm
  Posted by armando on 2016-05-30 16:43:00

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