Question

NO.1 Write the greatest 9-digit numbers using four different digits. Answer:-

Answer 1

If the three digits are d1<d2<d3d1<d2<d3 then

d3d3d3d3d3d3d3d2d1d3d3d3d3d3d3d3d2d1

is the largest possible nine digit number. If d1≠0d1≠0, then

d1d1d1d1d1d1d1d2d3d1d1d1d1d1d1d1d2d3

is the smallest, and if d1=0d1=0 and a nine digit number can't start with 0, then

d200000000d3d200000000d3

is the smallest.

The order of significance is always from left to right, which is a somewhat non-trivial fact. In other words, any nine-digit number is larger than any eight digit number.

You can prove that the pattern holds for any number of digits by induction.

Answer 2

Step-by-step explanation:

If the three digits are d1<d2<d3d1<d2<d3 then

d3d3d3d3d3d3d3d2d1d3d3d3d3d3d3d3d2d1

is the largest possible nine digit number. If d1≠0d1≠0, then

d1d1d1d1d1d1d1d2d3d1d1d1d1d1d1d1d2d3

is the smallest, and if d1=0d1=0 and a nine digit number can't start with 0, then

d200000000d3d200000000d3

is the smallest.

The order of significance is always from left to right, which is a somewhat non-trivial fact. In other words, any nine-digit number is larger than any eight digit number.

You can prove that the pattern holds for any number of digits by induction.