Digits
Posted: March 7th, 2017, 12:37 pm
This puzzle is to find a number whose square and cube, when taken together, contain all ten digits precisely once.
Cinelli
Cinelli
Shares, Investment and Personal Finance Discussion Forums
https://www.lemonfool.co.uk/
You can also observe that if the combination of square and cube include all ten digits, the digital root of this combination is 9. This further restricts the trial number to having a digital root of 3, 6, 8 and 9
psychodom wrote:The digital root (also repeated digital sum) of a non-negative integer is the (single digit) value obtained by an iterative process of summing digits, on each iteration using the result from the previous iteration to compute a digit sum. The process continues until a single-digit number is reached.
properties of digital roots
dr(a+b) = dr(dr(a) + dr(b))
dr(a*b) = dr(dr(a) * dr(b))