Take any four-digit number.
Create a second number by moving the first digit to the 'back of the queue' and moving the rest along.

Try it a few times. Is the answer always a multiple of $11$?
Can you explain why?

Click below to see what Samira noticed:

"I started with 5 thousands, 2 hundreds, 3 tens and 8 units.
After I moved the digits along, my new number had 2 thousands, 3 hundreds, 8 tens and 5 units.

I wonder if this can help me explain what's happening?"

Click below to see what Jay noticed:

"I picked 1000 as my first number, so my second number was 0001 and the total was 1001.
I know 1001 is a multiple of 11 because it is 1100-99, and 1100 and 99 are both multiples of 11."
The passage contains a mathematical question about whether the result of a specific operation on a four-digit number is always a multiple of 11, and it includes observations from Samira and Jay that provide insights into the problem.
single_question_with_answer
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
Take any four-digit number.
Create a second number by moving the first digit to the 'back of the queue' and moving the rest along.

Try it a few times. Is the answer always a multiple of $11$?
Can you explain why?

Click below to see what Samira noticed:

"I started with 5 thousands, 2 hundreds, 3 tens and 8 units.
After I moved the digits along, my new number had 2 thousands, 3 hundreds, 8 tens and 5 units.

I wonder if this can help me explain what's happening?"

Click below to see what Jay noticed:

"I picked 1000 as my first number, so my second number was 0001 and the total was 1001.
I know 1001 is a multiple of 11 because it is 1100-99, and 1100 and 99 are both multiples of 11."
user
The passage contains a mathematical question about whether the result of a specific operation on a four-digit number is always a multiple of 11, and it includes observations from Samira and Jay that provide insights into the problem.

TYPE: SINGLE_QUESTION_WITH_ANSWER