The image contains a math problem in Catalan related to forming two-digit numbers using the digits 2, 6, and 7. Here's a breakdown of the task:

Problem Description (Translated from Catalan):

Title: Form Numbers
Numbers with Two Digits
We want to know all the two-digit numbers that can be formed using the digits 2, 6, and 7.

Questions:

a) How many two-digit numbers can be formed?

Answer: You can form __ two-digit numbers.

b) How many different two-digit numbers can be formed?

Answer: You can form __ different two-digit numbers.

Solution:

1. For part (a):
   Each two-digit number can be formed by choosing a digit for the tens place and another digit for the ones place.
   Since we have the digits 2, 6, and 7 available, there are 3 choices for the tens place and 3 choices for the ones place.
   Thus, the total number of possible two-digit numbers (including repetitions) is:

$3 \times 3 = 9$

So, there are 9 possible two-digit numbers.

2. For part (b):
   Here, we are asked to form two-digit numbers where the two digits are different.
   For the tens place, we still have 3 choices, but once we pick a digit for the tens place, we have only 2 remaining choices for the ones place (since the digits must be different).
   Therefore, the total number of two-digit numbers with different digits is:

$3 \times 2 = 6$

So, there are 6 different two-digit numbers.

Final Answers:

• (a) There are 9 two-digit numbers in total.
• (b) There are 6 different two-digit numbers.

Would you like further details or have any other questions?

Additional Related Questions:

1. What are all the possible two-digit numbers that can be formed?
2. How many three-digit numbers can be formed using the same digits 2, 6, and 7?
3. Can we form any palindromic numbers using the digits 2, 6, and 7?
4. How many even two-digit numbers can be formed using these digits?
5. If you include the number 1 as a possible digit, how many two-digit numbers can be formed?

Tip: Always consider if digits can be repeated or not, as it significantly changes the number of possibilities!