TUTORIAL 1.1Minggu 2

Agnes Chong Tze YanAlex Ngu Ing Loong

Chua Bao YingTeoh Teik Yong

Twelve couples have been invited to a party. The couples will be seated at series of small square tables that can seat one person on each side. The tables are placed end to end so as to form one large long table. How many of these small tables are needed to seat all 24 people.

• Understand the problem

24 peoples are invited to a party. They are seated at square tables which can accommodate 1 person on each side of the table. The tables are joined at the edge to form a large long table. How many tables are needed to accommodate 24 persons?

• Planning the strategy

When the tables are joined, the tables can only accommodate 2 persons and 3 persons according to the positions of the tables.The tables at the edge can accommodate 3 persons while the tables in the middle can accommodate 2 persons.

• Execuate the strategy

Table with 2 persons = 9Table with 3 persons = 2

9 + 2 = 11 tables

• Checking the solution

Table with 2 persons = 9 x 2 = 18 personsTable with 3 persons = 2 x 3 = 6 persons

18 + 6 = 24 tables

There are 12 people in a small tutorial group. At the start of the semester they shake hands to introduce themselves. How many handshakes altogether?

Solution 1:2 33 4 44 5 55 6 66 7 7

Person 1 7 Person 2 8 Person 3 88 9 99 10 1010 11 1111 12 1212 and so on…

Therefore, 11+10+9+8+7+6+5+4+3+2+1= 66

Solution 2:By using calculator:

12C2 = 66

A family of four wants to cross a river by boat. The family consists of the father, mother, brother and sister. The boat can only carry one adult or one or two children at a time. Find the minimum number of ways in which the family can get across.

First, both children will go to the opposite side.

Then, the sister will wait at the shore while his brother sail back to the original side.

After that, the boy will get down from the boat and the father will ride the boat to the other side.

The father will get down from the boat and the sister will sail back to the original side.

Then, the brother together with the sister will sail back to the shore.

Then, the sister will get down and the brother will sail back to the original side in order to fetch her mother.

Then, the mother will sail to the opposite side and leave her son at the original side.

Then, the mother will get down and the sister will go and fetch her brother.

Lastly, both children will sail back to the shore and meet up with their parents.

Using the numerals 1,7,7,7 and 7 (a "1" and four "7"s) create the number 100.

As well as the five numerals you can use the usual mathematical operations +, -, x, ÷ and brackets ( ).

1. Understanding the question

Using a "1" and four "7"s create the number 100. Usual mathematical operations +, -, x, ÷ and brackets ( ) can also be used.

2. Carry out the solution

• Solution 1: 177 – 77 = 100

• Solution 2: (7 + 7) × (7 + (1 ÷ 7)) = 100