How many 4-digit numbers abcd are there such that a < b < c < d and b - a < c - b < d - c ?

Step-by-step solution

aligned & a < b < c < d & b-a < c-b < d-c aligned possibilities are aligned & a=1, b=2, c=4, d=7 & a=1, b=2, c=4, d=8 & a=1, b=2, c=4, d=9 & a=1, b=2, c=5, d=9 & a=1, b=3, c=6, d= no possible & a=2, b=3, c=5 d=8 & a=2, b=3, c=5 d=9 & a=2, b=3, c=6, d= not possible & a=3, b=4, c=6, d=9 & a=4, b=5, c=7, d= not possible aligned Ans. 7