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7

Step 1 Step 2 Step 3 And the mutual sum is $86$, as required.


0

I would approach it more like: (or in text:) Such that the lines are: Which gives us a result of:


0

I interpreted the problem to mean that there should be 5 rows of 4 consecutive trees remaining; to maximize the number of cut-down trees, we should make the remaining rows overlap as much as possible. If the rows must be of consecutive trees, you can arrange the remaining trees like this: So there are 5 rows of 4 consecutive palm trees; and we have done so ...


10

Thinking about this problem in reverse is easier, i.e. think about the trees that need to remain. Find the fewest number of trees that can be arranged in five lines with 4 trees in each line. To minimise that number, we need as many trees as possible to do double duty by being part of multiple lines.


0

Consider the mini-arrangement of trees below: The final arrangement of trees after chopping everything down should look something like this:


5

I found/figured out the solution. Starting with the reference to this problem here: http://www.chesshistory.com/winter/winter44.html#CN_5449 A few entries down the page, a more illuminating further reference is given: http://www.chesshistory.com/winter/winter44.html#CN_5455 This latter entry shows the crucial mating position: White knights on g3 and e0, ...


3

I start by excluding mating positions. If white King steps to e0 from e1 (from a normal stalemate position) the black king is outside of the red line and once the white king is on e0 there will be no attacking piece to deliver mate. If the position is not the stalemate illustrated above, but with one of the knights attacking, then white king doesn`t need to ...


-1

I don't think there can be a shortcut for the general version of the puzzle; if there were, you could very likely use the shortcut to solve the bin packing problem, which is known to be NP-hard. Finding a shortcut for solving that problem would prove that P equals NP, which would net you a million dollars on the spot. This means that your best shot for a ...


1

Your question is a bit confusing, but here some answers : We always need a passenger in the shutle, in boyh way. since Terry is at the limit capacity, he is always alone on the shutle, whitch mean that we need someone in the station to get the last pilot after Terry, since Terry can't be the last one. Here how you can do it : I can't prove that it is the ...


0

My analysis: To summarise:


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