You may also like

problem icon

Lesser Digits

How many positive integers less than or equal to 4000 can be written down without using the digits 7, 8 or 9?

problem icon


Consider all two digit numbers (10, 11, . . . ,99). In writing down all these numbers, which digits occur least often, and which occur most often ? What about three digit numbers, four digit numbers and so on?

problem icon

The Codabar Check

This article explains how credit card numbers are defined and the check digit serves to verify their accuracy.

Six Times Five

Age 11 to 14 Challenge Level:

No correct solution to this problem was originally received. However, Mary of Birchwood Community High School gave a sound argument that just needs some adaptation. Thank you Mary..

Firstly Mary considered the number of six digit numbers - this is 900,000.

10% of all six digit numbers start with a 5. So 90,000 six digit numbers are of the form 5******

This leaves 810,000 numbers that do not start with a 5. How many of these have a 5 as the second digit??

And so on.....

Here is a solution to this toughnut from Junwei of BHASVIC

Let the six digits number is abcdef, which a, b, c, d ,e, f represent a digit respectively.

For a, neither 0 nor 5 could place in it, thus, 8 digits are available here (1,2,3,4,6,7,8,9)

For b, c, d, e and f, they can't contain 5, hence, 9 digits are available for them (0,1,2,3,4,6,7,8,9)

Therefore, the no. of six digits number which does not contain any 5 is

8 * 9 * 9 * 9 * 9 *9 =472392 .