Finding a Specific Number Based on Conditions
<p>Let the three-digit number be represented as \( xyz \), where \( x, y, z \) are its digits.</p>
<p>According to the problem, if we append the digit 2 to the right of \( xyz \), we form the number \( xyz2 \).</p>
<p>We require that \( xyz2 > 4106 \).</p>
<p>Express \( xyz2 \) as \( 1000x + 100y + 10z + 2 \).</p>
<p>Thus, we want to find \( 1000x + 100y + 10z + 2 > 4106 \).</p>
<p>By simplifying, we have \( 1000x + 100y + 10z > 4104 \).</p>
<p>Dividing through by 10 gives \( 100x + 10y + z > 410.4 \).</p>
<p>Since \( 100x + 10y + z \) is an integer, it must be at least 411 for the condition to hold.</p>
<p>Therefore, we need to find all three-digit combinations \( xyz \) such that \( 100x + 10y + z \geq 411 \).</p>
<p>Based on the constraints of digit values from 0 to 9, we can deduce suitable values for \( x, y, z \).</p>
