<ol>
<li>30, 10, 67, 15
The four numbers above need to be put into descending order from left to right. The arrangement can only be changed in two ways: numbers with one or more numbers between them can be switched with each other, or the number in the farthest right position can be moved to the farthest left position. What is the least number of changes necessary in order to accomplish this.</li>
</ol>
<p>Just glancing at this quickly, I see that it can be done with 6 changes. Here’s one way:</p>
<p>1, 30, 10, 67, 15
10, 30, 1, 67, 15
10, 67, 1, 30, 15
15, 10, 67, 1, 30
30, 15, 10, 67, 1
1, 30, 15, 10, 67
67, 30, 15, 10, 1</p>
<p>I don’t have time to look at carefully right now. I’ll try to look at it again later today. This is an interesting problem. Where did you get it from?</p>
<p>btw the number 1 isnt in the set of four numbers
the set is 30, 10, 67, 15</p>
<p>That little nugget of information definitely changes the answer. Specifically where did you find this question? I would like to know as well. Anyways, assuming that you mean when moving the farthest right to the farthest left everything is simply moved right and/or values farthest left and right can also simply be swapped:
30 10 67 15
15 30 10 67
10 30 15 67
67 30 15 10
So 3 steps.</p>
<p>I honestly dont know where it came from
I think it is Princeton 2006 psat book but i am not sure
my teacher gave me the test</p>
<p>If considering the ‘moving far left position to far right’ as simply switching the 2 numbers, you get 3 steps as the smallest as well:</p>
<p>start: 30 10 67 15</p>
<p>step1: 30 15 67 10 (switched 10 and 15; between 1 number)
step2: 67 15 30 10 (switched 30 and 67; between 1 number)
step3: 10 15 30 67 (switched 67 and 10; between 2 numbers; far left to right, or vice versa)</p>
<p>Emidank, just a word of caution: the problem states that the numbers need to be in descending order from left to right. In this case, the answer still works out correctly, but this is not the case with every problem. I’m just saying this to make sure you don’t make a common mistake that has cost many people precious points.</p>
<p>Oops, my fault.</p>
<p>In that case, the correct way:</p>
<p>start: 30 10 67 15</p>
<p>step1: 15 10 67 30 (switched 15 and 30)
step2: 15 30 67 10 (switched 30 and 10)
step3: 67 30 15 10 (switched 67 and 15)</p>
<p>Yeah, three steps.
START: 30 10 67 15
15 10 67 30 (1)
10 15 67 30 (2)
10 15 30 67 (3) Done.</p>