The digital sum of an integer is the sum of all its digits. A digit sum sequence is a sequence of numbers that start with any integer and has each number after the first equal to the digital sum of the number before it. e.g. 7598, 29, 11, 2. Any digital sum sequence ends in a single digit number called the final digital sum or FDS.
Find and justify a rule that produces all 3 digit multiples of 7 with an FDS of 7
Find and justify a rule that produces all 3 digit multiples of 8 with an FDS of 8

Question

The digital sum of an integer is the sum of all its digits. A digit sum sequence is a sequence of numbers that start with any integer and has each number after the first equal to the digital sum of the number before it. e.g. 7598, 29, 11, 2. Any digital sum sequence ends in a single digit number called the final digital sum or FDS.
Find and justify a rule that produces all 3 digit multiples of 7 with an FDS of 7
Find and justify a rule that produces all 3 digit multiples of 8 with an FDS of 8

anonymous · Answer

i worked out the answers for the largest even and odd is 966 and 833

anonymous · Answer

and the largest 3 digit multiple of 7 which has a FDS (final digital sum) of 7 is 952