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標題: math question for help [打印本頁]

作者: chauch 時間: 08-12-23 11:43 標題: math question for help

Can anybody help?

A pack of biscuits to be shared equally among
3 children --> 2 biscuits left
5 children --> 3 biscuits left
7 children --> 4 biscuits left

What is the minimum number of biscuits in that pack of biscuits

作者: baekdoosan 時間: 08-12-23 11:54

answer: 53

作者: chauch 時間: 08-12-23 11:57 標題: 回覆 # 的文章

Thank you.
Can you show us the steps in reaching the answer.

作者: baekdoosan 時間: 08-12-23 14:44

N = 2(mod3)
N = 3(mod5)
N = 4(mod7)

5x7 = 35 is the smallest no. which is divisible by 5 and 7 and has remainder of 2 when divided by 3

3x7 = 21 is the smallest no. which is divisible by 3 and 7 and has a remainder of 1 when divided by 5
therefore 21x3 = 63 is divisible by 3 and 7 and has a remainder of 3 when divided by 5

3x5 = 15 is the smallest no. which is divisible by 3 and 5 and has a remainder of 1 when divided by 7
therefore 15x4 = 60 is divisible by 3 and 5 and has a remainder of 4 when divided by 7

LCM 3x5x7 = 105

N = 35+63+60 + 105t where t is integer
N = 158 + 105t (general solution)
N = 53 is smallest when (t = -1)

作者: chauch 時間: 08-12-23 15:39 標題: 回覆 # 的文章

Thanks very much.

作者: mandy_lee 時間: 08-12-24 11:41

原帖由 chauch 於 08-12-23 15:39 發表
Thanks very much.

幾年班maths 題目

作者: chauch 時間: 08-12-24 13:23 標題: 回覆 # 的文章

It's just an I.Q. math question for a P 5 student. We can get to the answer by simple logical thinking (trial by error), but the approach posted by baekdoosan is obviously beyond primary or even secondary school level.

作者: Heidibaba 時間: 08-12-25 00:02

三人同行七十稀
五樹梅花廿一枝
七子團圓正半月
餘百零五便得知

三三數之，餘數乘以七十
五五數之，餘數乘以廿一
七七數之，餘數乘以十五
三者相加，如不大於一百零五，即為答案；否則須減去一百零五或其倍數

(金庸．射鵰英雄傳)

原帖由 chauch 於 08-12-23 11:43 發表
Can anybody help?

A pack of biscuits to be shared equally among
3 children --> 2 biscuits left
5 children --> 3 biscuits left
7 children --> 4 biscuits left

What is the minimum number of biscuits i ...

作者: yanfaidaddy 時間: 08-12-25 00:46 標題: 回覆 # 的文章

wa, hohowanwoo.....

不如用個最原始的方法:

分三份餘二, 即:
5, 8, 11, 14... 47, 50, 53

分五份餘三, 即:
8, 13, 18, 23.. 43, 48, 53

分七份餘四, 即:
11, 18, 25, 31... 39, 46, 53

作者: sallyfung001 時間: 09-1-20 21:08

I prefer 最原始的方法!

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