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?
This list below contains some repeat numbers from the original list, but also some new numbers, enabled by allowing a unary negative sign at the beginning:
24 -24r^! -2^sqrt(4)!
120 -120!+!+! (-1+(2+0!)!)!
127 -127^+ -1+2^7
143 -14!3!*+ -1+4!*3!
144 -14+!4!* (-1+4)!*4!
324 -32r*4^ (-3*sqrt(2))^4
343 -34-3!^r sqrt((-3-4)^3!)
595 -59r!!+5!- -5+sqrt(9)!!-5!
713 -71*3!!+ -7*1+3!!
720 -72^r0!-! (sqrt(-7^2)-0!)!
729 -72-9r!^r sqrt((-7-2)^sqrt(9)!)
1294 -12*9r!4^+ -1*2+sqrt(9)!^4
1432 -14*3!!+2* (-1*4+3!!)*2
1433 -14r3!!*+3!- -1+sqrt(4)*3!!-3!
1434 -14r-3!!+4r* (-1-sqrt(4)+3!!)*sqrt(4)
1435 -14+!!3!!+5- (-1+4)!!+3!!-5
1436 -14*3!!+6!+ -1*4+3!!+6!
1439 -14r3!!r*9r!!r*+ -1+sqrt(4)*sqrt(3!!)*sqrt(sqrt(9)!!)
1440 -14+!!4r* (-1+4)!!*sqrt(4)
1441 -14+!!4r*1+ (-1+4)!!*sqrt(4)+1
1442 -14+!!4r*2+ (-1+4)!!*sqrt(4)+2
1443 -14r4r3!!+*+ -1+sqrt(4)*(sqrt(4)+3!!)
1444 -14+!!4r+4r* ((-1+4)!!+sqrt(4))*sqrt(4)
1445 -14+!!4r*5+ (-1+4)!!*sqrt(4)+5
1446 -14+!!4r*6+ (-1+4)!!*sqrt(4)+6
1447 -14+!!4r*7+ (-1+4)!!*sqrt(4)+7
1448 -14+!!4r*8+ (-1+4)!!*sqrt(4)+8
1449 -14r-4!^rr9r!!+ sqrt(sqrt((-1-sqrt(4))^4!))+sqrt(9)!!
1463 -14!+6!+3!!+ -1+4!+6!+3!!
1464 -14+!!6!+4!+ (-1+4)!!+6!+4!
1673 -16-7!3/+ -1-6+7!/3
1679 -16!7*9r/+ -1+6!*7/sqrt(9)
1764 -17r*6r*4^ (-1*sqrt(7)*sqrt(6))^4
1944 -19r!rr*4!^4!/ (-1*sqrt(sqrt(sqrt(9)!)))^4!/4!
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Posted by Charlie
on 2016-05-31 08:40:44 |
Supplement to part 1 list
