1. Peter has a weigh balance with two pans
Peter has a weigh balance with two pans. He also has one 200g weight and one 1000g weight. He wants to take 600g of sugar out of a pack containing 2000g of sugar. What is the minimum number of moves to accomplish this task?
Solution:
Answer: 1 𝑚𝑜𝑣𝑒
To make it balance, each pan should have
= 𝟐𝟎𝟎𝒈+𝟐𝟎𝟎𝟎𝒈+𝟏𝟎𝟎𝟎𝒈 𝟐
=𝟏𝟔𝟎𝟎 𝒈
This also means 𝟔𝟎𝟎𝒈 needs to be moved to the left pan.

2. In the figure below, 𝐸𝐵 𝐵𝐷 = 1 2 and the area of the shaded part is 42cm2. Find the area of ABC ?
Solution:
Because 𝐸𝐵 𝐵𝐷 = , therefore area for
∆𝑩𝑪𝑬= 1 2 ∆𝑩𝑪𝑫
∆𝑨𝑩𝑬= 1 2 ∆𝑨𝑩𝑫
∴∆𝑨𝑩𝑪= 𝒐𝒇 𝒔𝒉𝒂𝒅𝒆𝒅 𝒂𝒓𝒆𝒂= ______ 𝒄𝒎 𝟐

3. In the diagram, there are two touching circles, each of radius 2 cm
In the diagram, there are two touching circles, each of radius 2 cm. An ant starts at point A and walks around the figure 8 path ABCDEFCGA in that order. The ant repeats the figure 8 walk, again and again. After the ant has walked a distance of 2005𝜋 cm it becomes tired and stops. The ant stops at a point in the path. What letter point is it?
Solution:
The distance between two adjacent points is:
= 2𝜋 ×2 4
= 𝜋 𝑐𝑚
The distance for every figure ‘8’ travelled =8𝜋 𝑐𝑚
2005𝜋÷8𝜋=250 𝑟𝑒𝑚𝑎𝑖𝑛𝑖𝑛𝑔 _____
Answer: stop at point _____

4. During recess one of the five pupils wrote something nasty on the blackboard. When questioned by the class teacher, they answered in following order:
A: “It was B and C.”
B: “Neither E nor I did it.”
C: “A and B are both lying.”
D: “Either A or B is telling the truth.”
E: “D is not telling the truth.”
The class teacher knows that three of them never lie while the other two may lie. Who wrote it?
Solution:
If A wrote it: A lie, B truth, C lie, D truth, E lie; 3 person lied ⇒𝑁𝑜𝑡 𝑡ℎ𝑒 𝑐𝑎𝑠𝑒
If B wrote it: A truth, B lie, C lie, D truth, E lie; 3 person lied ⇒𝑁𝑜 𝑡ℎ𝑒 𝑐𝑎𝑠𝑒
If C wrote it: A truth, B truth, C lie, D truth, E lie; 2 person lied ⇒𝐴𝑛𝑠𝑤𝑒𝑟
If D wrote it: A lie, B truth, C lie, D truth, E lie; 3 person lied ⇒𝑁𝑜 𝑡ℎ𝑒 𝑐𝑎𝑠𝑒
If E wrote it: A lie, B lie, C truth, D lie, E truth; 3 person lied ⇒𝑁𝑜 𝑡ℎ𝑒 𝑐𝑎𝑠𝑒