<h1>Accepted Solution:</h1>
<pre><code>"A" // initial render of `A`
"B" // initial render of `B`
// `App` re-renders due to the state update triggered by `userEvent.click(screen.getByText('click me'))`
"A" // memoized `A` re-renders when `App` re-renders because its `children` prop has changed
// memoized `B` does not re-render when `App` re-renders because its props have not changed
</code></pre>
<h1>Explanation</h1>
<h2>Key Takeaways:</h2>
<ul>
<li>A component normally re-renders when its parent re-renders.</li>
<li>A memoized component will not always re-render when its parent re-renders unless its props have changed, including the <code>children</code> prop.</li>
<li>A component passed as props (i.e. <code>children</code>) to its parent component that renders it, belongs to the component where it is instantiated and passed to its parent, not the parent itself.</li>
<li>Memoizing a component with <code>React.memo</code> does not prevent it from returning a new object reference</li>
<li>Memoizing a component with the hook <code>useMemo</code> can ensure that it returns the same object reference if the hook's dependencies don't change</li>
</ul>
<h2>Solution Breakdown:</h2>
<h3>Initial Render</h3>
<ol>
<li>Component <code>App</code> renders for the first time.</li>
<li>Component <code>A</code> renders for the first time, logging <strong><code>"A"</code></strong>.</li>
<li>Component <code>B</code> renders for the first time, logging <strong><code>"B"</code></strong>.</li>
</ol>
<h3>After Button Click</h3>
<ol>
<li>
<p><strong>Component <code>App</code>'s state (</strong><code>count</code><strong>) is updated, causing it to re-render.</strong>
<code>userEvent.click(screen.getByText('click me'))</code> calls the onClick handler, <code>() =&gt; setCount(count =&gt; count + 1)</code>, which schedules a state update in <code>App</code>, causing <code>App</code> to re-render, because <strong>state updates trigger re-renders</strong>.</p>
</li>
<li>
<p><strong>During the re-render of component <code>App</code>, component <code>A</code> receives a new <code>children</code> prop because <code>&lt;B /&gt;</code> always returns a new React element (object) every time component <code>App</code> renders.</strong>
Even though component <code>B</code> is rendered by component <code>A</code>, since component <code>B</code> is instantiated in component <code>App</code>, where it is passed to component <code>A</code> through the <code>children</code> prop, component <code>B</code> technically belongs to component <code>App</code> and always computes to a new object value (even when it is not re-rendered) every time component <code>App</code> renders. This means that every time component <code>App</code> re-renders, the <code>children</code> prop of component <code>A</code> is always reassigned to a new value.</p>
</li>
<li>
<p><strong>Because the <code>children</code> prop of component <code>A</code> always changes every time component <code>App</code> re-renders, component <code>A</code> also re-renders, because its props have changed, thereby logging <strong><code>"A"</code></strong> again.</strong></p>
</li>
<li>
<p><strong>Component <code>B</code> does not re-render when component <code>App</code> re-renders, because it is memoized and its props did not change.</strong>
Even though component <code>B</code> is technically rendered by component <code>A</code>, it is instantiated in component <code>App</code>, where it is passed to component <code>A</code> through the <code>children</code> prop. <strong>A component passed as props (i.e. <code>children</code>) to its parent component that renders it, belongs to the component where it is instantiated and passed to its parent, not the parent itself.</strong> This means that component <code>B</code> technically belongs to component <code>App</code> and would normally re-render when component <code>App</code> re-renders. However, component <code>B</code> does not re-render when component <code>App</code> re-renders, because it is memoized and its props have not changed.</p>
</li>
</ol>
<h2>Why component <code>B</code> always returns a new <code>children</code> prop value to component <code>A</code> when component <code>App</code> re-renders, even when component <code>B</code> does not re-render because it is memoized by React.memo</h2>
<p>To understand why the <code>children</code> prop of component <code>A</code> always returns a new value for component <code>B</code> (<code>&lt;B /&gt;</code>) every time component <code>App</code> re-renders, remember that JSX is simply syntactic sugar for the <code>React.createElement(component, props, ...children)</code> function, which returns an object. Memoizing a component with <code>React.memo</code> returns a memoized version of this function (as long as the components props don't change), not the object it outputs. Therefore, every time component <code>App</code> re-renders, component <code>B</code>, <code>&lt;B /&gt;</code>, compiles to a memoized version of <code>React.createElement(B, null)</code> because its props have not changed, which does not re-render but always returns a new object, albeit with identical values as before.</p>
<p>This new object is passed to component <code>A</code> through the <code>children</code> prop. Because component <code>A</code> is memoized, it does not automatically re-render when its parent component, <code>App</code>, re-renders. Instead, React performs a shallow comparison of its props to determine if it should re-render. In JavaScript, a shallow comparison of objects evaluates only reference equality, not structural equality. In other words, it checks if two objects point to the same instance in memory, not if they have the same properties and values. Therefore, every time component <code>App</code> re-renders, the <code>children</code> prop of component <code>A</code>, translates to a new object instance returned by <code>React.createElement(B, null)</code>, which fails the shallow comparison test, causing component <code>A</code> to re-render.</p>
<h3>React.memo vs. useMemo</h3>
<p><code>useMemo</code> is a React Hook that caches the result of a calculation between re-renders and returns a memoized value if its dependencies don't change.</p>
<p>If component <code>B</code> was memoized with <code>useMemo</code> inside component <code>App</code>, instead of <code>React.memo</code>, and passed to component <code>A</code> through the <code>children</code> prop, component <code>A</code> would not re-render when component <code>App</code> re-renders.  Component <code>B</code>, which compiles to <code>React.createElement(B, null)</code> and returns an object,  would return the same cached object reference that passes the shallow comparison test of component <code>A</code>'s props. Thus, component <code>A</code> would not re-render.</p>
<pre><code>function _B() {
  console.log('B')
  return null
}

const B = memo(_B)

function _A({ children }) {
  console.log('A')
  return children
}

const A = memo(_A)

function App() {
  const [count, setCount] = useState(0);
  const memoizedB = useMemo(() =&gt; (
    &lt;B /&gt;
  ), []);
  
  return &lt;div&gt;
    &lt;button onClick={
      () =&gt; setCount(count =&gt; count + 1)
    }&gt;
      click me
    &lt;/button&gt;
    &lt;A&gt;{ memoizedB }&lt;/A&gt;
  &lt;/div&gt;
}
</code></pre>
<p>Console Output:</p>
<pre><code>"A"
"B"
</code></pre>
<p>Test it yourself in <a href="https://codepen.io/xtini/pen/rNgdqeW?editors=1111">Codepen</a></p>

Detailed Explanation (Updated)

What does the code snippet to the right output by console.log?…