Determine the minimum value of a positive integer N that satisfy the following conditions:
- N is a multiple of 101.
- N starts with and ends in 98.
- sod(N) = 94
*** sod(N) denotes the sum of the digits of N.
For example, sod(3456) = 3+4+5+6 = 18
[
Edit: Ignore this comment]
N = k*101
Since 101 ends with 01, k must end in 98
Since 101 begins with 10, k must begin in either 97 or 98
---- [Edit: this solution was totally incorrect, so please ignore it.]
So all multipliers of the form 98abc...xyz98 * 101 will satisfy the first 2 requirements. [Edit: provided they are multiples of 101]
Also most multipliers of the form 97abc...xyz98 will satisfy these criteria, except when the middle portion is very small, for example 970098, 970198, 970298 do not work but all other 97xx98 options do work.
if the sod is to be 94 the first 2 and last 2 digits so far sum to 33 or 34 which leaves 60 or 61 still needed.
97799999998 and 98699999998 both do the trick, but the smallest is:
97799999998 [incorrect]
Edited on July 3, 2023, 3:26 pm
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Posted by Larry
on 2023-07-03 11:24:30 |
Analytic solution
