The given problem presents a pattern where two numbers are combined in a unique way to produce a six-digit number. To solve this, we need to understand the pattern behind the operation of combining the two numbers.

We observe:

• $23 + 82 = 106411$
• $32 + 42 = 151613$
• $46 + 34 = 408113$

Analysis of the Pattern

Let's break down each resulting six-digit number based on the inputs.

1. First part:

   • In $23 + 82 = 106411$, the first two digits "10" seem to correspond to the sum $23 + 82 = 105$, so it might represent the first digit(s) of the sum of the two numbers.

   • Similarly, for $32 + 42 = 151613$, the sum is $32 + 42 = 74$, and the first digits are "15". It could be possible that the sum is multiplied by some factor or added with a constant to give the first three digits.

   • In $46 + 34 = 408113$, the sum $46 + 34 = 80$, and we see "408" as the first three digits.

2. Second part:

   • The middle two digits of each result appear to be consistently connected to the two individual numbers.
     • In $23 + 82 = 106411$, "41" might be derived from $23 \times 2 = 46$ or some similar rule.
     • Similarly, "16" in the second case and "81" in the third case likely follow a similar transformation rule related to the original numbers.

3. Last part:

   • The last two digits appear unrelated to the sum and might be directly linked to the second number.

Given these clues, let's predict the six-digit number for $71 + 26$.

Prediction for $71 + 26$:

• First part: $71 + 26 = 97$, and following a pattern similar to "15", "408", we might guess the first few digits are 971.

• Second part: Based on transformations seen earlier, the middle two digits could correspond to a modified form of $71$, resulting in something like 61.

• Last part: We could guess the last two digits based on the transformations from 26, giving us something like 13.

Thus, the number formed could be:

$971613$

Therefore, $71 + 26 = 971613$.

---

Would you like further details on the breakdown of the pattern?

Related Questions:

1. How would you determine a consistent rule for the middle two digits?
2. Can we generalize this pattern for any two numbers?
3. What happens if we use different two-digit numbers? Would the pattern hold?
4. How is this problem related to modular arithmetic or base conversions?
5. Could there be a connection to a cryptographic or number-theoretic function?

Tip: Always look for common properties or transformations when dealing with number patterns.