Digit sums of whole numbers – an analysis


Every morning on my way to office, I had to drive through the whole Aizawl city from Mission Veng to Chaltlang. I could not help looking at the registration numbers of cars in front or of those parked on the roadsides, such as, for example, MZ 01 D 2143, MZ 01 E 8379, MZ 01 F 5617, etc. All car numbers are four digit whole numbers. As a man of mathematics, I often add up the digits in my mind, noting the various sums of the digit numbers viz. 10, 27, 19 (for the above 3 car numbers). A thought came to me that the lowest possible sum for a 4-digit number would be 1 corresponding to which all possible registration numbers that can be allotted are 4 (four), viz. 0001, 0010, 0100 and 1000. It is also clear that for a given alphabet, all possible car registration numbers that can be allotted would be 9999 altogether, viz. MZ 01 F 0001 ... F 9999. The next car after F 9999 will have to be allotted G 0001 and so on.

Full Text Download