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Show that you can arrange a copies of all 3r ternary strings so that two consecutive strings differ in one position, and the last string

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Show that you can arrange a copies of all 3\"r ternary strings so that two consecutive strings differ in one position, and the last string and first string aiso differ in one position. For example, with n = 2, 11,21,22, 12, 32, 12, 22, 23,33, 31, 21,11,13,23,13, 33, 32, 31 is one such arrangement

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