Question

6636 | 3
8118 | 4
2212 | 0
8688 | ?
5971 | ?

Explanation:

Step1: Analyze the pattern for each number

For \(6636\): Count the number of closed loops (holes) in each digit. \(6\) has 1 loop, \(6\) has 1 loop, \(3\) has 0, \(6\) has 1. Total loops: \(1 + 1+ 0 + 1 = 3\), which matches the right number.

Step2: Check \(8118\)

\(8\) has 2 loops, \(1\) has 0, \(1\) has 0, \(8\) has 2. Total: \(2 + 0 + 0 + 2 = 4\), matches.

Step3: Check \(2212\)

\(2\) has 0, \(2\) has 0, \(1\) has 0, \(2\) has 0. Total: \(0\), matches.

Step4: Solve for \(8688\)

\(8\) (2) + \(6\) (1) + \(8\) (2) + \(8\) (2) = \(2 + 1 + 2 + 2 = 7\)? Wait, no, wait: Wait, \(6\) has 1 loop, \(8\) has 2. Wait, let's re - calculate:
\(8\): 2 loops, \(6\): 1 loop, \(8\): 2 loops, \(8\): 2 loops. Sum: \(2 + 1+2 + 2=7\)? Wait, no, wait the first number \(6636\): digits are 6,6,3,6. Each 6 has 1 loop, 3 has 0. So 1 + 1+0 + 1 = 3. Correct. \(8118\): 8 (2) + 1 (0)+1 (0)+8 (2)=4. Correct. \(2212\): 2 (0)+2 (0)+1 (0)+2 (0)=0. Correct. Now \(8688\): 8 (2) + 6 (1)+8 (2)+8 (2)=2 + 1+2 + 2 = 7? Wait, no, wait maybe I made a mistake. Wait \(8\) has 2 loops, \(6\) has 1. Let's check again:
For \(8688\):
Digit 8: 2 loops
Digit 6: 1 loop
Digit 8: 2 loops
Digit 8: 2 loops
Total loops: \(2 + 1+2 + 2=7\)? Wait, but let's check the next number \(5971\):
Digit 5: 0 loops
Digit 9: 1 loop (the circle in 9)
Digit 7: 0 loops
Digit 1: 0 loops
Total loops: \(0 + 1+0 + 0 = 1\)

Wait, let's re - check the loop counts:

• 0: 1 loop
• 6: 1 loop
• 8: 2 loops
• 9: 1 loop
• 1,2,3,4,5,7: 0 loops

Ah! I made a mistake earlier. Let's re - calculate with correct loop counts:

For \(6636\):
Digits: 6 (1), 6 (1), 3 (0), 6 (1). Sum: \(1 + 1+0 + 1 = 3\) (correct).

For \(8118\):
Digits: 8 (2), 1 (0), 1 (0), 8 (2). Sum: \(2 + 0+0 + 2 = 4\) (correct).

For \(2212\):
Digits: 2 (0), 2 (0), 1 (0), 2 (0). Sum: \(0\) (correct).

For \(8688\):
Digits: 8 (2), 6 (1), 8 (2), 8 (2). Sum: \(2 + 1+2 + 2 = 7\)? Wait, no, wait 8 has 2 loops, 6 has 1. Wait 2+1 + 2+2 = 7? Wait, but let's check \(5971\):

Digits: 5 (0), 9 (1), 7 (0), 1 (0). Sum: \(0 + 1+0 + 0 = 1\)

Wait, let's re - do \(8688\):

8: 2, 6:1, 8:2, 8:2. So 2 + 1+2 + 2 = 7? Wait, but maybe the pattern is the number of times a digit with a loop appears? No, the sum of loops.

Wait, another way: Let's list the loop - bearing digits:

• 0: 1 loop
• 6: 1 loop
• 8: 2 loops
• 9: 1 loop

So for \(8688\):

8 (2) + 6 (1) + 8 (2) + 8 (2) = 2+1 + 2+2 = 7? Wait, no, 2 + 1 is 3, 3+2 is 5, 5 + 2 is 7.

For \(5971\):

5 (0) + 9 (1) + 7 (0) + 1 (0) = 1.

Wait, let's confirm with the first three numbers:

\(6636\): 6 (1) * 3 + 3 (0) = 3. Correct.

\(8118\): 8 (2)2 + 1 (0)2 = 4. Correct.

\(2212\): all non - loop digits, sum 0. Correct.

So the pattern is: sum the number of loops in each digit of the 4 - digit number, where:

• 0: 1 loop
• 6: 1 loop
• 8: 2 loops
• 9: 1 loop
• 1,2,3,4,5,7: 0 loops

Now, for \(8688\):

Digits: 8 (2), 6 (1), 8 (2), 8 (2)

Sum: \(2 + 1+2 + 2 = 7\)

For \(5971\):

Digits: 5 (0), 9 (1), 7 (0), 1 (0)

Sum: \(0 + 1+0 + 0 = 1\)

Answer:

For \(8688\), the answer is \(7\); for \(5971\), the answer is \(1\)