CODEWITHSUNDEEP
c#algorithmcountdigits
Nick Farsi
Nick Farsi

Reputation: 427

Count number of lucky numbers in triskaideca numeral system

Consider 13-digit numbers in 13-decimal numeral system (0,1,2,3,4,5,6,7,8,9,A,B,C) with leading zeros:

ABA98859978C0, 6789110551234, 0000007000000

Consider a number lucky if sum of it's first 6 digits == sum of it's last 6 digits

0055237050A00 - lucky => 0+0+5+5+2+3 = 0+5+0+A+0+0
1234AB988BABA - unlucky => 1+2+3+4+A+B != 8+8+B+A+B+A

Task: Write a program that'd count amount of all 13-digit lucky numbers in 13-decimal numeral system

What would be the way to solve this? I can only think about going from

BigInteger.Parse("-13131313131313131313131313") (that would be minimal possible value = -CCCCCCCCCCCCC)

to

BigInteger.Parse("13131313131313131313131313") (that would be maximal possible value = CCCCCCCCCCCCC)

in a loop and checking whether or not the criteria meets, but that's probably not optimal

Upvotes: 1

Views: 315

Answers (1)

samgak
samgak

Reputation: 24427

Iterate through all possible 6-digit numbers and make a count of how many numbers add up to each possible sum. You can store this in an array with 73 elements ((6 x 12) + 1). For each sum n with m numbers adding to n, there will be m x m x 13 lucky 13-digit numbers where the first and last 6 digits both sum to n (each of the m numbers can be in the first 6 digits in combination with each of the m numbers in the last 6 digits, and the 7th digit can be anything). Sum up the total for each possible sum and that's your overall total.

Upvotes: 2

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