Some Summed Digits In A 9-Digit Positive Integer

[K Sengupta]

Determine a 9-digit positive integer that uses each of the decimal digits from 1 to 9 exactly once, such that:

(i) The sum of the digits 1 and 2 and all the digits between them is 9.

(ii) The sum of the digits 2 and 3 and all the digits between them is 20.

(iii) The sum of the digits 3 and 4 and all the digits between them is 45.

(iv) The sum of the digits 4 and 5 and all the digits between them is 18.

(v) The sum of the digits 8 and 9 and all the digits between them is more than 32.

(vi) The 8^th digit is less than the 2^nd digit.

 

[Jimmy Snyder]

Spoiler

495162783

 

[K Sengupta]

Well done JS !

I came across this problem in a puzzle periodical. However, the original version only provided clues (i) to (iv). I added clues (v) and (vi) on my own with a view to eliciting an unique solution.

I am just thinking aloud, but keeping all the other conditions unaltered, that is, 9-digit positive integer, using all the digits 1 to 9 exactly once, and so on ……, are there positive nondecimal integer base(s) A, with 11<= A <= 16, such that A gives at least one valid solution to the given problem !