2000年AMC10竞赛第17题
$$2000-AMC10-17$$  Boris has an incredible coin changing machine. When he puts in a quarter, it returns five nickels; when he puts in a nickel, it returns five pennies; and when he puts in a penny, it returns five quarters. Boris starts with just one penny. Which of the following amounts could Boris have after using the machine repeatedly?  鲍里斯有一台令人难以置信的硬币更换机。 当他投入$$25$$美分时，它返回五个$$5$$分币； 当他投入$$1$$个五分硬币时，它返回$$5$$个人$$1$$分硬币； 当他投入一分钱时，它会返回五个$$25$$美分硬币。 鲍里斯从一分钱开始。 鲍里斯在反复使用机器后可能会获得以下哪些金额？
课内体系->知识点->函数的应用->函数与方程 美国AMC10/12->Knowledge Point->Algebra->Application->Equation Word Problems
Consider what happens each time he puts a coin in. If he puts in a quarter, he gets five nickels back, so the amount of money he has doesn\textquotesingle t change. Similarly, if he puts a nickel in the machine, he gets five pennies back and the money value doesn\textquotesingle t change. However, if he puts a penny in, he gets five quarters back, increasing the amount of money he has by~~cents.  This implies that the only possible values, in cents, he can have are the ones one more than a multiple of . Of the choices given, the only one is D 