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<p><strong>Explanation:</strong> Alice can pick up <code>3</code> ones in <code>3</code> moves, if Alice performs the following actions in each move when standing at <code>aliceIndex == 1</code>:</p>
<ul>
<li>&nbsp;At the start of the game Alice picks up the one and <code>nums[1]</code> becomes <code>0</code>. <code>nums</code> becomes <code>[1,<strong><u>1</u></strong>,1,0,0,1,1,0,0,1]</code>.</li>
<li>At the start of the game Alice picks up the one and <code>nums[1]</code> becomes <code>0</code>. <code>nums</code> becomes <code>[1,<strong><u>0</u></strong>,0,0,0,1,1,0,0,1]</code>.</li>
<li>Select <code>j == 2</code> and perform an action of the first type. <code>nums</code> becomes <code>[1,<strong><u>0</u></strong>,1,0,0,1,1,0,0,1]</code></li>
<li>Select <code>x == 2</code> and <code>y == 1</code>, and perform an action of the second type. <code>nums</code> becomes <code>[1,<strong><u>1</u></strong>,0,0,0,1,1,0,0,1]</code>. As <code>y == aliceIndex</code>, Alice picks up the one and <code>nums</code> becomes&nbsp;<code>[1,<strong><u>0</u></strong>,0,0,0,1,1,0,0,1]</code>.</li>
<li>Select <code>x == 0</code> and <code>y == 1</code>, and perform an action of the second type. <code>nums</code> becomes <code>[0,<strong><u>1</u></strong>,0,0,0,1,1,0,0,1]</code>. As <code>y == aliceIndex</code>, Alice picks up the one and <code>nums</code> becomes&nbsp;<code>[0,<strong><u>0</u></strong>,0,0,0,1,1,0,0,1]</code>.</li>
<li>Select <code>x == 2</code> and <code>y == 1</code>, and perform an action of the second type. <code>nums</code> becomes <code>[1,<strong><u>1</u></strong>,0,0,0,1,1,0,0,1]</code>. As <code>y == aliceIndex</code>, Alice picks up the one and <code>nums</code> becomes <code>[1,<strong><u>0</u></strong>,0,0,0,1,1,0,0,1]</code>.</li>
<li>Select <code>x == 0</code> and <code>y == 1</code>, and perform an action of the second type. <code>nums</code> becomes <code>[0,<strong><u>1</u></strong>,0,0,0,1,1,0,0,1]</code>. As <code>y == aliceIndex</code>, Alice picks up the one and <code>nums</code> becomes <code>[0,<strong><u>0</u></strong>,0,0,0,1,1,0,0,1]</code>.</li>
</ul>
<p>Note that it may be possible for Alice to pick up <code>3</code> ones using some other sequence of <code>3</code> moves.</p>
@@ -40,9 +40,9 @@
<ul>
<li>Select <code>j == 1</code> and perform an action of the first type. <code>nums</code> becomes <code>[<strong><u>0</u></strong>,1,0,0]</code>.</li>
<li>Select <code>x == 1</code> and <code>y == 0</code>, and perform an action of the second type. <code>nums</code> becomes <code>[<strong><u>1</u></strong>,0,0,0]</code>. As <code>y == aliceIndex</code>, Alice picks up the one and <code>nums</code> becomes&nbsp;<code>[<strong><u>0</u></strong>,0,0,0]</code>.</li>
<li>Select <code>x == 1</code> and <code>y == 0</code>, and perform an action of the second type. <code>nums</code> becomes <code>[<strong><u>1</u></strong>,0,0,0]</code>. As <code>y == aliceIndex</code>, Alice picks up the one and <code>nums</code> becomes <code>[<strong><u>0</u></strong>,0,0,0]</code>.</li>
<li>Select <code>j == 1</code> again and perform an action of the first type. <code>nums</code> becomes <code>[<strong><u>0</u></strong>,1,0,0]</code>.</li>
<li>Select <code>x == 1</code> and <code>y == 0</code> again, and perform an action of the second type. <code>nums</code> becomes <code>[<strong><u>1</u></strong>,0,0,0]</code>. As <code>y == aliceIndex</code>, Alice picks up the one and <code>nums</code> becomes&nbsp;<code>[<strong><u>0</u></strong>,0,0,0]</code>.</li>
<li>Select <code>x == 1</code> and <code>y == 0</code> again, and perform an action of the second type. <code>nums</code> becomes <code>[<strong><u>1</u></strong>,0,0,0]</code>. As <code>y == aliceIndex</code>, Alice picks up the one and <code>nums</code> becomes <code>[<strong><u>0</u></strong>,0,0,0]</code>.</li>
</ul>
</div>