英语翻译1、The number of diagonals that can be drawn in a regular

英语翻译
1、The number of diagonals that can be drawn in a regular polygon with twenty sides（icosagon）is ( )
2、The greatest number of Mondays,which can occur in 45 consecutive days,is ( )
3、You have 3 weights:1kg,3kg,9kg as well as an equal arm balance,as shown.How many different weight objects can you weigh with these three?
4、The least natural number whose digits sum equals 100,is ( )

1、The number of diagonals that can be drawn in a regular polygon with twenty sides (icosagon)is ( )
翻译：正20边形的对角线有几条?
用组合计算,20选2 = 190,然后减去20条边,190 - 20 = 170
2、The greatest number of Mondays,which can occur in 45 consecutive days,is ( )
翻译：连续45天内,最多有几个星期一?
把第一天当成星期一,45-1=44,6×7=42,接下去还会出现6次,6+1=7
最多有7个星期一.
3、You have 3 weights:1kg,3kg,9kg as well as an equal arm balance as shown.
How many different weight objects can you weigh with these three?
翻译：如图所示,你有1千克、3千克、9千克三个砝码,还有一个两臂等长的天平.
用这三个砝码,最多能称出多少种不同重量的物体?
因为不知道图形如何,只能按一般常规情况解答.
组合：三选一 = 3,三选二 = 3,三选三 = 1,3+3+1=7,7种.
这7种结果中没有重复的数字,所最多是7种.
4、The least natural number whose digits sum equals 100,is ( )
翻译：各个位数相加的和等于100,这样的自然数中,最小的是多少?
要找最小的自然数,第一考虑的是位数必须最少.
要位数最少,每个位数上的数字必须越大越好.
100÷9=11.1111.,最多可有11个9,100-99=1,
所以,符合条件的最小自然数是199,999,999,999
也就是1999亿9999万9999.