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Outdoor & Recreation
Camping
Maths problem to solve while sitting around the campfire?
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<blockquote data-quote="BigWave" data-source="post: 580271" data-attributes="member: 6786"><p>Sorry RM. </p><p>Doesn't work for all starting positions.</p><p>PS: Imagine that there are two distinct Cases: </p><p>1: The mouse was in an even numbered box when you open your first. </p><p>2: The mouse was in an odd numbered box when you open your first. </p><p>Let's now start by considering Case 1 - that it must be even in an numbered box (ie: 2 or 4). </p><p>Clearly, you'd pick an even numbered box first. </p><p>If you picked 2 and it was in there (you win in 1 move), but if it was in box 4 (you lose that round). </p><p>Next time the mouse would be in box 3 or 5. </p><p>If your next pick was in box 3 and it was there, then you win that round (in 2 moves), but if it were in box 5 you lose.</p><p>So, if it was in box 5 yesterday, you'd pick box 4 today (so you win in 3 moves)</p><p>The opening order so far is: 2, 3, 4 (or it could have been 4,3,2) with the same result.</p><p>These are the only 2 sequences that will work for Case 1 (even numbered starting positions).</p><p>But what if it starts in an odd-numbered box?</p></blockquote><p></p>
[QUOTE="BigWave, post: 580271, member: 6786"] Sorry RM. Doesn't work for all starting positions. PS: Imagine that there are two distinct Cases: 1: The mouse was in an even numbered box when you open your first. 2: The mouse was in an odd numbered box when you open your first. Let's now start by considering Case 1 - that it must be even in an numbered box (ie: 2 or 4). Clearly, you'd pick an even numbered box first. If you picked 2 and it was in there (you win in 1 move), but if it was in box 4 (you lose that round). Next time the mouse would be in box 3 or 5. If your next pick was in box 3 and it was there, then you win that round (in 2 moves), but if it were in box 5 you lose. So, if it was in box 5 yesterday, you'd pick box 4 today (so you win in 3 moves) The opening order so far is: 2, 3, 4 (or it could have been 4,3,2) with the same result. These are the only 2 sequences that will work for Case 1 (even numbered starting positions). But what if it starts in an odd-numbered box? [/QUOTE]
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Outdoor & Recreation
Camping
Maths problem to solve while sitting around the campfire?
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