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?
(In reply to
Part 1 redone allowing unary negation by Charlie)
24 2n4r^! ((-(2))^sqrt(4))!
36 3!6* (3)!*6
71 7!1+r sqrt(((7)!+1))
119 1n1n9r!+!+ -(1)+((-(1)+(sqrt(9))!))!
120 1n2n0!-n!+! ((-(1)+((-((-(2)-(0)!))))!))!
127 1n2n7^- -(1)-(-(2))^7
143 1n4!n3!*- -(1)-(-((4)!))*(3)!
144 1n4+!4!* ((-(1)+4))!*(4)!
145 14!+5!+ 1+(4)!+(5)!
216 21+!r6^ sqrt(((2+1))!)^6
240 2n4!n0!-nr!n* (-(2))*(-((sqrt((-((-((4)!)-(0)!)))))!))
324 3!2r/4^ ((3)!/sqrt(2))^4
343 3n4-3!^r sqrt((-(3)-4)^(3)!)
354 3n5!n4r+* (-(3))*(-((5)!)+sqrt(4))
355 3n5!n*5- (-(3))*(-((5)!))-5
360 3n6n0!+n!n* (-(3))*(-(((-((-(6)+(0)!))))!))
384 3!rr8r*4^ (sqrt(sqrt((3)!))*sqrt(8))^4
456 4n5!n6+* (-(4))*(-((5)!)+6)
595 5n9r!!+5!- -(5)+((sqrt(9))!)!-(5)!
693 6!9rrn3!^- (6)!-(-(sqrt(sqrt(9))))^(3)!
713 7n1n3!!*- -(7)-(-(1))*((3)!)!
715 71-!5- ((7-1))!-5
720 7n2-0!n*r!! ((sqrt(((-(7)-2)*(-((0)!)))))!)!
721 72+r!!1+ ((sqrt((7+2)))!)!+1
722 72+r!!2+ ((sqrt((7+2)))!)!+2
723 72+r!!3+ ((sqrt((7+2)))!)!+3
724 72+r!!4+ ((sqrt((7+2)))!)!+4
725 72+r!!5+ ((sqrt((7+2)))!)!+5
726 72+r!!6+ ((sqrt((7+2)))!)!+6
727 72+r!!7+ ((sqrt((7+2)))!)!+7
728 72+r!!8+ ((sqrt((7+2)))!)!+8
729 7n2-9r!^r sqrt((-(7)-2)^(sqrt(9))!)
733 73!!+3!+ 7+((3)!)!+(3)!
736 73n6^+ 7+(-(3))^6
744 7n4!-4!n* (-(7)-(4)!)*(-((4)!))
936 9r!r3!^6!+ sqrt((sqrt(9))!)^(3)!+(6)!
1285 1n2n8^-5n* (-(1)-(-(2))^8)*(-(5))
1288 12+!r8^8- sqrt(((1+2))!)^8-8
1294 1n2n9r!n4^+n* (-(1))*(-((-(2)+(-((sqrt(9))!))^4)))
1296 12+!r9r!^6* sqrt(((1+2))!)^(sqrt(9))!*6
1298 1n2n*9r!rn8^+ (-(1))*(-(2))+(-(sqrt((sqrt(9))!)))^8
1392 13+!9r!!-2n* (((1+3))!-((sqrt(9))!)!)*(-(2))
1432 1n4n*3!!-2n* ((-(1))*(-(4))-((3)!)!)*(-(2))
1433 1n4rn3!!*-3!- -(1)-(-(sqrt(4)))*((3)!)!-(3)!
1434 1n4r-3!!+4r* (-(1)-sqrt(4)+((3)!)!)*sqrt(4)
1435 1n4r*3!!n*5- (-(1))*sqrt(4)*(-(((3)!)!))-5
1436 1n4n3!!+n*6!+ (-(1))*(-((-(4)+((3)!)!)))+(6)!
1439 1n4rn3!!*- -(1)-(-(sqrt(4)))*((3)!)!
1440 1n4r*40!-!!n* (-(1))*sqrt(4)*(-((((4-(0)!))!)!))
1441 1n4+!!4r*1+ (((-(1)+4))!)!*sqrt(4)+1
1442 1n4rn4-n!-2n* (-(1)-((-((-(sqrt(4))-4))))!)*(-(2))
1443 1n4rn4r3!!+*- -(1)-(-(sqrt(4)))*(sqrt(4)+((3)!)!)
1444 1n4+!!4r+4r* ((((-(1)+4))!)!+sqrt(4))*sqrt(4)
1445 1n4+!!4r*5+ (((-(1)+4))!)!*sqrt(4)+5
1446 1n4+!!4r*6+ (((-(1)+4))!)!*sqrt(4)+6
1447 1n4+!!4r*7+ (((-(1)+4))!)!*sqrt(4)+7
1448 1n4+!!4r*8+ (((-(1)+4))!)!*sqrt(4)+8
1449 1n4+!!4r*9+ (((-(1)+4))!)!*sqrt(4)+9
1463 1n4!+6!+3!!+ -(1)+(4)!+(6)!+((3)!)!
1464 1n4r*6!n*4!+ (-(1))*sqrt(4)*(-((6)!))+(4)!
1573 1n5!-7n3!-* (-(1)-(5)!)*(-(7)-(3)!)
1673 1n6-7!n3n/+ -(1)-6+(-((7)!))/(-(3))
1679 1n6!n7n*n9r/- -(1)-(-(((-((6)!))*(-(7)))))/sqrt(9)
1680 16+!8n0!-nr/ ((1+6))!/sqrt((-((-(8)-(0)!))))
1704 1n7!-0!n*r4!* sqrt(((-(1)-(7)!)*(-((0)!))))*(4)!
1764 1n7r*6r*4^ ((-(1))*sqrt(7)*sqrt(6))^4
1944 1n9r*4!rr*4^ ((-(1))*sqrt(9)*sqrt(sqrt((4)!)))^4
Edited on June 2, 2016, 7:46 am
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Posted by Charlie
on 2016-06-02 07:31:32 |
Part 1 down to 67 entries after eliminating the spurious
