SAT MATH QUESTION 1） The sum of eleven different integers is zero.What is the least number of these integers that must be positive?2) In a certain game,each token has one of three possible values:1 point,5points or 10points.How many different combinations of these token values are worth a total of 17 points?
问题描述：
SAT MATH QUESTION
1） The sum of eleven different integers is zero.What is the least number of these integers that must be positive?
2) In a certain game,each token has one of three possible values:1 point,5points or 10points.How many different combinations of these token values are worth a total of 17 points?
答
1) 答案是只需一个，且题目有无数解。
问题问最少有多少个有理数为正数，那么如果需要和为0的话，正有理数和要等于负有理数的和的绝对值，那么便一定要有一个正有理数。我们知道，有理数相加，还是一个有理数，所以任何10个负有理数相加，都可以找出一个正有理数，使绝对值相等。那么解题的话，随便选10个负有理数，取一个正有理数就可以得出来了。
2）第二题我看只能用枚举法，因为有无限个token, 不能用排列组合。解法就如一楼一样，一个一个试，有规律地试也就画30秒，在数学SAT中足够时间了。
答
1) 1
example:-10,-9,-8,-7,-6,-5,-4,-3,-2,-1,55
2) 6
all 1's,three 5's+two 1's,two 5's+seven 1's,one 5+twelve 1's,one 5+one 10+two 1's,one 10+seven 1's