Question

How many positive four-digit integers consist of four digits that are consecutive integers in increasing or decreasing order

Answer 1

For increasing order: 6

For decreasing order:7

Explanation:

Case (1):

When the four digits are the consecutive integers in increasing order, then the possible digits at the thousands place (digit 4) are 1,2,3,4,5, and 6.

The numbers formed are 1234, 2345, 3456, 4567, 5678, and 6789.

Therefore, there are 6 four-digit positive integers for increasing order of consecutive digit.

Note that 0 can't be placed at the thousands place to get a four-digit integer.

Case(2):

When the four digits are the consecutive integers in decreasing order, then the possible digits at the unit place (digit 1) are 0, 1,2,3,4,5, and 6.

The numbers formed are 3210, 4321, 5432, 6543, 7654, 8765, 9876.

Therefore, there are 7 four-digit positive integers for decreasing order of consecutive digit.