In a certain game ,each token has one of three possible valu

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In a certain game ,each token has one of three possible values:1 point,5 points,or 10 points.How many different combinations of these token values are worth a total of 17 points?

题目翻译：在一个游戏中,每种筹码（代币）有三种可能的数值：1分,5分,10分.如果要使这些筹码（代币）的总和为17分,请问一共有多少种不同的组合方法?
楼上说的枚举法可以,即列举法,你也可以列一个式子,用代入法分类解决.

列式：x+5y+10z=17.
1、当x=0时.5y+10z=17.
此时：没有整数解.
0种可能.
2、当y=0时.x+10z=17.
此时：①x=17.17个1分.
②x=7,y=1.7个1分,1个10分.
两种可能.
3、当z=0时.x+5y=17.
此时：①x=17.这个条件与y=0时重复,舍去.
②x=12,y=1.12个1分,1个5分.
③x=7,y=2.7个1分,2个5分.
④x=2,y=3.2个1分,3个5分.
4、当x、y、z全不为0时.x+5y+10z=17.
此时：①x=2,y=1,z=1.2个1分,1个5分,1个10分.
综上所述,一共六种可能.
PS：不要信广告哦~有其他问题可以留言,祝好运~

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