*15x2*
=-5-4-3-2-1+0+1+2+3+4+5+6+7+8+9
=6+7+8+9
Monday, 9 March 2015
每周数学 (十二): Consecutive Sums 21/03/2015
Wednesday, 4 March 2015
每周数学(十一): Traffic Jam (also know as Fishing Boat or Leap-Frog) 14/03/2015
*Fishing boat*
Ten Men are fishing from a boat, five in the front, five in the back, and there is one empty seat in the middle.
The five in front are catching all the fish, so the five at the back want to change seats.
To avoid capsizing the boat, they agree to do so using the following rules:
1.A man may move from his seat to and empty seat next to him.
2.A man may step over only one man to an empty seat.
3.No other move are allowed.
What is the minimum number of moves necessary for the men to switch places?
If there are n men from each side, how many moves is needed for the swap?
*渔船*
十个人在船上钓鱼,五个在前面,五个在后面,中间有一个空座位。
前面的五个人都有鱼获,所以后面的五个人想换座位。
为避免翻t船,他们同意使用以下规则:
1.一个人可以从他的座位移动到他旁边的空座位。
2.个人只能跨过另一人到一个空位。
3.不允许其他动作。
交换位置所需的最少移动次数是多少呢?
*如果双方各有 n 个人,交换需要多少个步骤?*
Leapfrog
no of no of no of total no
pegs slides Jumps Moves
1. 2. 1. 3
2. 4. 4. 8
3. 6. 9. 15
4. 8. 16. 24
n. 2n. n^2. n(n+2)
Strategic:
1. Simplify the problems
2. Critical concepts, critical moves?
3. Total shifts : 2n(n+1)
Jumps: n^2
1 jump =2 shifts
Total Slides
= Totalshifts-2x total jumps
= 2n(n+1)-2n^2
=2n
Tuesday, 3 March 2015
每周数学(九) :The Tower of Hanoi 河内之塔 28/02/2015
Weekly Maths 8: Sum to 20 21/02/2015
Weekly Maths 7 : The Three Mathematicians 14/02/2015
Weekly Maths 6 : Fibonacci Magic 07/02/2015
Weekly Maths 5 :The Singapore Polytechnic Lockers 31/01/2015
每周数学(四):韩信点兵 24/01/2015 Remainder Theorem
24/01/2015
淮安民间传说着一则故事——“韩信点兵”,其次有成语“韩信点兵,多多益善”。韩信带1500名兵士打仗,战死四五百人,站3人一排,多出2人;站5人一排,多出4人;站7人一排,多出6人。韩信马上说出人数:1049。
在一千多年前的《孙子算经》中,有这样一道算术题:“今有物不知其数,三三数之剩二,五五数之剩三,七七数之剩二,问物几何?”按照今天的话来说:一个数除以3余2,除以5余3,除以7余4,求这个数。这样的问题,也有人称为“韩信点兵”。它形成了一类问题,也就是初等数论中的解同余式。
①有一个数,除以3余2,除以4余1,问这个数除以12余几?
②一个数除以3余2,除以5余3,除以7余2,求符合条件的最小数。
1。《孙子算经》下巻26题
“今有物不知其数,三三数之剩二,五五数之剩三,七七数之剩二,问物几何?
2。韩信带1500名兵士打仗,战死四五百人,站3人一排,多出2人;站5人一排,多出4人;站7人一排,多出6人。韩信马上说出人数:.......。
解法:余数定理
参考资讯;余数定理
http://youtu.be/1LZ1Hqaw8BY
http://youtu.be/IRHuYTS6r68
http://episte.math.ntu.edu.tw/articles/sm/sm_01_01_2/page6.html
言兵莫过孙武,用兵莫过韓信
西汉·司马迁《史记·淮阴侯列传》:上问 曰:“如我能将几何?”信曰:“陛下不过能 将十万。”上曰:“子有何如?”曰:“臣多 多而益善耳。”
典故:
胯下之辱
成也萧何,败也萧何!
韓信点兵;多多益善!
明修栈道,暗渡陈仓;
背水一战;十面埋伏.....
谢谢建平同学提供...
每周数学(三):百钱买百鸡🐔17/01/2015 Problem of the hundred Fowls
Maths Questions for your children
👍誏儿孙们思考的数学!
Q1. 百钱買百鸡
今有鸡翁一,值钱伍;鸡母一,值钱三;鸡鶵三,值钱一。凡百钱买鸡百只,问鸡翁、母、 鶵各几何?
我特别喜欢古代数学家张丘建在《算经》一书中提出的这数学问题。有好多解法!也有好几个答案;(非学校传统式的標准试题)(又含人生哲理)
Q2. 和尚食饅头
一百个和尚吃一百个饅头
大和尚一人食三个,小和尚三人吃一个饅头。问大小和尚各几人?
💝
请享受解题的美妙过程!无穷乐趣。
Please enjoy the thinking process, the approaches and concepts. 😄
祝福安康
每周数学(二):The CHOCOLATE BARS。10/01/2015
Maths Questions for your children
👍誏儿孙们思考的数学!
Q1. A Mathematics teacher had a certain number of CHOCOLATE BARS, he gave them to the top three students as prizes.
The top students received two third of the chocolate bars plus one third of a bar , the second student received two third of the remaining plus one third of a bar, and the third student received two third of the remaining plus one third of a bar and had received only one bar of chocolate.
How many chocolate bars did the teacher have initially?
Q2 Similar to question 1,
If the teacher have to give away chocolate bars as prizes to 4 or 5 top students, how many chocolate bars must he have?
Q3 Similarly, what happen if the pattern of 2/3 changes to 3/4 or 4/5?
💝
请享受解题的美妙过程!
Please enjoy the thinking process, the approaches and concepts. 😄
祝福安康
每周数学(一): PSLE2000 03/01/2015
Maths Questions for ....
👍给....的数学题目!
Q1. What is the last digit of the sum from 1 to 97?
有几个解法?
(Year 2000 PSLE Q15)👌
Q2. Magic SQ 3x3, and 4x4 怎样解?
💝
请享受解题的美妙过程!
Please enjoy the process, the approaches and concepts. 😄
Q1
1。成人解法
S=n(n+1)/2.......
2。儿童解法
1
2
3+97=100
4+96=100
5+95=100
.
.
48+52=100
49+51=100
50
Answer: 3
.
Q2.
1+2+......+9=9x10/2=45
45/3=15
9+1+5 =15
9+2+4 =15