Problem Solving

Question

how many more 4 digit even numbers than 4 digit odd nunbers can be formed using only digit from the set (0, 1, 6)?

Answer 1

Using the fundamental counting principle.

To generate 4 digit numbers there are only two numbers to pick from for the thousand's digit (1 and 6).

For the hundredth's digit you can use any of the 3 (0, 1, 6).

For the tenth's digit, same thing, any of the 3

For odd four digit numbers there is only 1 number that can be used for the unit's digit (1).

For even four digit numbers there are two choices (0 or 6).

That means the number of even 4 digit numbers can be calculated as:

2 ⋅ 3 ⋅ 3 ⋅ 2 = 36

The number of odd 4 digit numbers:

2 ⋅ 3 ⋅ 3 ⋅ 1 = 18

So there are twice as many even 4 digit numbers as odd 4 digit numbers. Or specifically 18 more.

Some examples:

Even

1000

1006

1100

1106

1110

1116

1600

1610

.....

6000

6006

6666

Odd

1001

1011

1061

1101

1111

1161

1601

1611

1661

...

6661

Listing both sets would not be too difficult, but using fundamental counting principle makes it a lot easier.