Mr. Digit wanted to assign a number to each student in his class. He could only use the digits 2,3,and 6 and each student's number had to have three digits. Can he find enough numbers for all 25 students if repeated digits are allowed? Will there be any extra numbers?

Question

Mr. Digit wanted to assign a number to each student in his class. He could only use the digits 2,3,and 6 and each student's number had to have three digits. Can he find enough numbers for all 25 students if repeated digits are allowed? Will there be any extra numbers?

Answer 1

There may be a shortcut to finding this answer -- but you can do it this way:

222
223
226
232
233
236
262
263
266
Do the same with numbers beginning with 3 and 6.

Answer 2

Or you could just count how many numbers Ms. Sue provided and multiply by three for your total number of possiblities.

Answer 3

To determine if Mr. Digit can find enough numbers for all 25 students, we need to find out the total number of possible numbers he can create with the given digits.

For each digit in a three-digit number, there are three possibilities (2, 3, or 6) since repeated digits are allowed. Therefore, the total number of possible three-digit numbers using these digits is calculated by multiplying the number of possibilities for each digit: 3 * 3 * 3 = 27.

Mr. Digit can create 27 different three-digit numbers using the digits 2, 3, and 6.

Since the total number of numbers he can create (27) is greater than the number of students (25), Mr. Digit can find enough numbers for all 25 students. In fact, there will be 2 extra numbers (27 - 25 = 2) available.