https://notexponential.com/qa/artificial-intelligence/uninformed-search Powered by Question2Answer https://notexponential.com/769/searching-problem-with-numbers?show=793#a793 This problem could be solved using UCS if we use a search tree with &#039;4&#039; as the root. The branching factor is 3 with each branch having a different cost.<br /> <br /> Let&#039;s use a notation of (&#039;node name&#039;,cost) when discussing this problem.<br /> <br /> (&#039;4&#039;,0) -&gt; [ (&#039;4&#039;,1), (&#039;2&#039;,2), (&#039;24&#039;,3) ]<br /> <br /> The (&#039;4&#039;,1) is suboptimal as a repeated value and the (&#039;2&#039;,2) node leads to a dead end due to the factorial.<br /> <br /> The best option is to choose (&#039;24&#039;,3) as the next item.<br /> <br /> (&#039;24&#039;,3) -&gt; [ (&#039;24&#039;,4), (&#039;4.89...&#039;,5), (&#039;24!&#039;,6) ]<br /> <br /> The (&#039;4.89...&#039;,5) leads to nodes &#039;2&#039; and &#039;4&#039; again based on the operations and the &#039;24&#039; node is the identity. We should continue with (&#039;24!&#039;,6).<br /> <br /> Since &#039;24!&#039; is a large number, we will certainly use the square root several times. Luckily, after 5 rounds, we get &#039;5.54&#039;, which the floor function can turn into the desired 5.<br /> <br /> (4,0) -&gt; (24,3) -&gt; (24!,6) -&gt; (sqrt(24!),8) -&gt; (sqrt(sqrt(24!),10) -&gt; (sqrt(sqrt(sqrt(24!)),12) -&gt; (sqrt(sqrt(sqrt(sqrt(24!)))),14) -&gt; (sqrt(sqrt(sqrt(sqrt(sqrt(24!)))),16) = (&#039;5.54&#039;,16) -&gt; (5,17)<br /> <br /> Thus, we can reach the desired state of &#039;5&#039; at a cost of 17 units. Uninformed Search https://notexponential.com/769/searching-problem-with-numbers?show=793#a793 Sat, 04 Mar 2023 21:47:13 +0000