2003年AMC10竞赛B第7题
$$[x]$$ 表示不超过$$x$$的最大整数$$.$$ 例如, $$[3]=3$$, $$\left[\frac 92\right]=4$$. 求$$[\sqrt 1]+[\sqrt 2]+[\sqrt 3]+\cdots +[\sqrt {16}]$$的值.
美国AMC10/12->Knowledge Point->Combination->Reasoning->Information Migration (new definition) 课内体系->知识点->函数的概念与性质->函数的概念及其表示->函数的概念->取整函数（高斯函数）
The first three values in the sum are equal to $$1$$, the next five equal to $$2$$, the next seven equal to $$3$$, and the last one equal to $$4$$, For example, since $$2^{2}=4$$ any square root of a number less than $$4$$ must be less than $$2$$. Sum them all together to get $$3\times 1+5\times 2+7\times 3+1\times 4=3+10+21+4=38$$. 