Question
U1 L1 Warm-Up: Create a Pattern
Place a digit in each blue box to create a pattern where the numbers change by the same amount each time. Use only the digits 0 to 9 without repeating any digits
Place a digit in each blue box to create a pattern where the numbers change by the same amount each time. Use only the digits 0 to 9 without repeating any digits
Answers
GPT-4o mini
To create a pattern where numbers change by the same amount each time, let's select an initial digit for the first blue box and determine the common difference for the pattern.
Let's say we place the digit **2** in the first blue box.
Now, let's create a pattern that increases by **3** each time.
1. First box: **2**
2. Second box: **2 + 3 = 5**
3. Third box: **5 + 3 = 8**
4. Fourth box: **8 + 3 = 11** (but we cannot use '11' since we are limited to digits 0 to 9)
So let's consider creating a pattern with a different common difference.
Now using a common difference of **4**:
1. First box: **1**
2. Second box: **1 + 4 = 5**
3. Third box: **5 + 4 = 9**
4. Fourth box: **9 - 4 = 5** (but we cannot repeat '5')
We need a new strategy. Let's start with **3**:
If we take the following sequence starting from **3** and increment by **2**:
1. First box: **3**
2. Second box: **3 + 2 = 5**
3. Third box: **5 + 2 = 7**
4. Fourth box: **7 + 2 = 9**
The resulting pattern is: **3, 5, 7, 9**
Now, if we want to ensure all digits are unique and all fall within 0-9, we can choose any box giving a unique number without repeating:
Here is a correct solution where numbers change by 1:
1. First box: **0**
2. Second box: **1**
3. Third box: **2**
4. Fourth box: **3**
Ultimately, a valid pattern can look like this:
**0, 1, 2, 3**
This way, it fulfills the criteria of unique digits without any repeats. You can choose other starting points and common differences as long as you don’t repeat any during the digits 0-9.
Let's say we place the digit **2** in the first blue box.
Now, let's create a pattern that increases by **3** each time.
1. First box: **2**
2. Second box: **2 + 3 = 5**
3. Third box: **5 + 3 = 8**
4. Fourth box: **8 + 3 = 11** (but we cannot use '11' since we are limited to digits 0 to 9)
So let's consider creating a pattern with a different common difference.
Now using a common difference of **4**:
1. First box: **1**
2. Second box: **1 + 4 = 5**
3. Third box: **5 + 4 = 9**
4. Fourth box: **9 - 4 = 5** (but we cannot repeat '5')
We need a new strategy. Let's start with **3**:
If we take the following sequence starting from **3** and increment by **2**:
1. First box: **3**
2. Second box: **3 + 2 = 5**
3. Third box: **5 + 2 = 7**
4. Fourth box: **7 + 2 = 9**
The resulting pattern is: **3, 5, 7, 9**
Now, if we want to ensure all digits are unique and all fall within 0-9, we can choose any box giving a unique number without repeating:
Here is a correct solution where numbers change by 1:
1. First box: **0**
2. Second box: **1**
3. Third box: **2**
4. Fourth box: **3**
Ultimately, a valid pattern can look like this:
**0, 1, 2, 3**
This way, it fulfills the criteria of unique digits without any repeats. You can choose other starting points and common differences as long as you don’t repeat any during the digits 0-9.