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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.)
Still there | Comment 5 of 10 |
Not much to add. A pair of interesting numbers under 2016 and some other over. 
The smart: 
729=(7+2)^sqrt9
720=6!=(7-2^0)!

The other is for factorials
40320=8!=(4+0+3+2^0)!
362880=9!=((3*6)-(2*8)+8+0)!

I did not see Charlie's two posts before this!

Edited on May 31, 2016, 7:36 am
  Posted by armando on 2016-05-31 07:32:43

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