小學

有一種舞蹈的舞步的一小節的動作是：左腳向左側點一下、右腳向右側點一下、進二步、退三步；左腳向左側點一下、右腳向右側點一下、進三步。以後不斷地循環以上的動作。若舞步每點一下、退一步、進一步都是一拍，請問一位舞者從開始的位置到達前方50步的位置為止，至少共須經過多少拍？

請問什麼是無窮級數？
請趕快解答，謝謝！

我發現了一個奇特的東西，任何一個正整數都可以是一或二、三或四個正整數的平方的和，舉例來說：
1=1*1（一個平方數）
2=1*1+1*1（二個平方數）
3=1*1+1*1+1*1（三個平方數）
4=2*2（一個平方數）
5=2*2+1*1（二個平方數）
6=2*2+1*1+1*1（三個平方數）
7=2*2+1*1+1*1+1*1（四個平方數）
......................................................................
210=11*11+5*5+7*7（三個平方數）
或14*14+2*2+3*3+1*1（四個平方數）
等等…………
為什麼會這樣呢？

請問十進制的0.5如何換成五進制來表示？其它進制呢？

On a true/flase test of 100 items, evey item number that is multiple of 4 is ture, and all other are flase, If a student marks every item that is multiple of 3 flase and all others ture, how many of the 100 items will be correctly answered?
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1的2006次方+2的2006次方+3的2006次方+4的2006次方+5的2006次方+6的2006次方+7的2006次方+8的2006次方+9的2006次方=?

N is a natural number such that when divided by 10 it leaves the remainder 9, when divided by 9 it leaves the remainder 8, when divided by 8 it leaves the remainder 7, ...., when divided by 2 it leaves the remainder 1. Find the smallest value of N.
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There are over 50 children sitting in a circle. They count clockwise around the circle starting from 1. If the same child has counted 2 and 2006, What is the least number of children in the circle?
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Solly wants to unlock his friend Koss's combination lock. the lock consists of 4 reels, each reel displays the digits from 1 to 9. Koos tells Solly that the first digit from left to right is a multiple of 3, the second digit is a prime, the third digit is a multiple of 2 and the whole unmber is divisible by 4. By following Koss' clues, waht is the maximum possible number of different ways that Solly can unclock it?
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The lengths of two sides of a triangle are 2006 and 6002 units respectively. If the length, in the sme units, of the third side of this triangle is and integer, how many different triangles can exist?
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