和冰墩墩一起挑战奥数，连上第七天

趁世界杯赛东风，「小离校」策划10期奥数终究，每日一道奥数题，文章区每天发票并积极参与咨询，坚持10天将获得我们校对的泰国奥数资料除此以外印刷版。 昨日口试解析

[英文原题]Una rolls 6 standard 6-sided dice simultaneously and calculates the product of the 6 numbers obtained. What is the probability that the product is divisible by 4？

中文简明如下，Una同时掷6个6面掷骰子，得到6位数，量度6位数的之和，问，这个之和被4正整数的权重是多少？

可以考虑之和很难被4正整数的权重，然后1-很难被4正整数的权重=之和能被4正整数的权重。

之和很难被4正整数可以细分2种情况：

一般而言1: 之和很难被2正整数。一个掷骰子掷出个数的权重为1/2，6个掷骰子都是个数的权重是1/64.

一般而言2：之和能被2正整数，但很难被4正整数。需要5个掷骰子为个数，一个掷骰子为个数。权重为

答案为1-（1/64+1/16）=59/64.

今日口试

A scientist walking through a forest recorded as integers the heights of 5 trees standing in a row. She observed that each tree was either twice as tall or half as tall as the one to its right. Unfortunately some of her data was lost when rain fell on her notebook. Her notes are shown below, with blanks indicating the missing numbers. Based on her observations, the scientist was able to reconstruct the lost data. What was the average height of the trees, in meters?

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