To solve the equation \( b + 62 = 62 + 1 \), we will first simplify the right side of the equation.
Calculating the right side:
\[ 62 + 1 = 63 \]
Now, our equation is:
\[ b + 62 = 63 \]
Next, we will subtract 62 from both sides to isolate \( b \):
\[ b + 62 - 62 = 63 - 62 \]
Simplifying both sides gives:
\[ b = 1 \]
Thus, the value of \( b \) that makes the addition sentence true is:
\[ \boxed{1} \]
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