Question 156
Suppose we have a 9-digit number $N$ in which all the digits are distinct and non-zero. Then we consider all the sums of adjacent triples of digits of $N$ and order them in a non-decreasing sequence. For the following sequences, determine whether there exists an $N$ for which we get them as a result:
a) $11, 15, 16, 18, 19, 21, 22,$
b) $11, 15, 16, 18, 19, 21, 23.$
a) $11, 15, 16, 18, 19, 21, 22,$
b) $11, 15, 16, 18, 19, 21, 23.$