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David Eppstein Geometry Junkyard suggested combining these problems.
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What is the fewest number of continuous arcs needed to pass through a grid of points? David shows that three arcs are enough for the 4x4 case. What's the answer for the 5x5?
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Solutions on the Connect the Dots page. Consider the following diagram of observers. The other observers are blocked.
Observer A can see six other observers. If I gave the problem, "Plant 11 observers so that 4 of them can see exactly 7 other observers," then the following diagram would work B E G I.
Cihan Altay sent me three Observer puzzles. As in the example above, observers can 'see' in any direction, not just along grid lines.
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The group of problems forms my puzzle of the week. A similar problem is to arrange 6 observers so that each one sees exactly 4 others. If you have n observers, and each one sees k or fewer others, how small can k be?
At Cihan's sitehe is currently running a competition problem: It starts Asagidaki diyagramdaki toplam Rearrange those 9 letters so that they form the ending of an 11 letter word describing a type of triangle. John Gowland has sent me some new datings site xx photo crossword. Tetris Squares, by John Gowland 1. In this game of Tetris, two sets of tetrominoes have fallen into a 5 by 8 grid.
Each piece contains the digits 1, 2, 3 and 4. Each row is a five digit number found by multiplying the unknowns together. Each unknown is a prime less than Double Squares was solved by Dwight Kidder. The 12x12 Peaceful Queens problem lead to an interesting range of solutions, as you can see above.
Nick and Bob even squeezed in an extra queen. As the diagrams above suggest, there is still much to be discovered. I'll gladly publish any results. A hundred problems in Dots and Boxes, with increasing difficulty.
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The third problem from the book is below, play and win. The 97 problems that follow are harder, several problems towards the end on a 5x5 board!
In addition, a full wealth of the known strategies are explained. He even provides a Nimbers calculatorfor more difficult positions.
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What is the winning move? No notation scheme is given in the book pictures are usedso I'll introduce one.
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Any move will be either the lower edge — or left edge of a given square. Such a scheme, for a 5x5 grid, would use A-F and Koshi Arai -- Make a numeric formula whose answer is using the 9 digits from 1 to 9 in that order. He also sent.
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