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Bellringer #7

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Bellringer #7

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  1. Prince Ivan made up his mind to fight the three-headed, three-tailed dragon. So he obtained a magic sword that could, in one stroke, chop off either one head, two heads, one tail, or two tails. A witch revealed the dragon’s secret to him: if one head is chopped off, a new head grows; in place of one tail, two new tails grow; in place of two tails, one new head grows; and if two heads are chopped off, nothing grows. What is the smallest number of strokes the Prince must make to chop off all the heads and tails? Bellringer #7

  2. Solution #7 • The answer is nine. After Prince Ivan makes h (n = 1,2) strokes that cope off n of the dragon’s heads and t . (k = 1, 2) strokes that chop off k tails, the numbers of heads and tails will be equal to 3-h + t and 3-t – 2t , respectively. So we must find the solution to the equations 2h – t = 3 and 2t – t = 3

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