Mathematical recreations and essays . ese 10 there are a such routes. In any such route we mayput each of the five doubles in any one of two positions (ex. gr. * Hence if we remove one domino, say 5-4, we know that the line formed bythe rest of the dominoes must end on one side in a 5 and on the other in a 4. 12—2 180 UNICURSAL PKOBLEMS [CH. IX in the route given above the double-two can be put between0-2 and 2-3 or between 1-2 and 2-4). Hence the totalnumber of unicursal arrangements of the 15 dominoes is 2^ we arrange the dominoes in a straight line, then as wemay begin
Mathematical recreations and essays . ese 10 there are a such routes. In any such route we mayput each of the five doubles in any one of two positions (ex. gr. * Hence if we remove one domino, say 5-4, we know that the line formed bythe rest of the dominoes must end on one side in a 5 and on the other in a 4. 12—2 180 UNICURSAL PKOBLEMS [CH. IX in the route given above the double-two can be put between0-2 and 2-3 or between 1-2 and 2-4). Hence the totalnumber of unicursal arrangements of the 15 dominoes is 2^ we arrange the dominoes in a straight line, then as wemay begin with any of the 15 dominoes, the total number ofarrangements is 15 . 2. a. We have next to find the number of unicursal routes ofthe pentagon delineated above in figure A. At the node 0there are four paths which may be coupled in three pairs. If01 and 0 2 are coupled, as also 0 3 and 0 4, we get figure 01 and 0 3 are coupled, as also 0 2 and 0 4, we get figure G,If 0 1 and 0 4 are coupled, as also 0 2 and 0 3, we get figure
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