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Shortest way to a million (Posted on 2020-12-03) Difficulty: 3 of 5
The number one million can be presented by 2 digits : 1000000, i.e. a chain of 7 digits.
Another possibility is 10002. 3 distinct digits, 5 characters. I

You are requested to express one million, using a single digit d plus some operators creating a chain of n characters ( digits and operators).
What digit is your choice and how low is the minimal n?

a). The permissible operators are : + - * / and ^.

b). Sqrt and ! are allowed as well.”

. REM: count digits and operators only, ignore ^, concatenation and brackets; e.g. (77-7)/7 is counted as 6.

No Solution Yet Submitted by Ady TZIDON    
Rating: 4.5000 (4 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Some Thoughts Best known of each digit | Comment 9 of 15 |
I'll update this list if people find more.  The number of counted characters is in brackets.

Part a).

(1111-111)^(1+1) and also (111-11)^(1+1+1) [11]

[2*(22^2 + 2^(2^2))]^2  [10] xdog

((33-3)/3)^(3+3) [9]

((44-4)/4)^((4+4)/4+4) [13]

(5+5)^(5+5/5) [8] xdog

((66-6)/6)^6 [7]

((77-7)/7)^(7-7/7) [11]

((88-8)/8)^(8-(8+8)/8) [13]

999999+9/9 [10]

Part b).  if an improvement is known

(11-1)^(1+1+1)!  [10] xdog
((33-3)/3)^3! [8]
(4+4+sqrt4)^(4+sqrt4) [10] Ady
(9+9/9)^((sqrt9)!) [8] Ady

Edited on December 4, 2020, 8:56 pm

Edited on December 7, 2020, 8:17 am
  Posted by Jer on 2020-12-04 12:56:10

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