1) Peter has a balance with 200g and 1000g weights and wants to remove 600g of 2000g sugar. The minimum moves is 1, which is to put the 200g and 1000g weights on one side and 600g sugar on the other. 2) A diagram shows two touching circles with radius 2cm. An ant walks a figure 8 path around the circles repeatedly. After walking 2005π cm, the ant stops at point C. 3) Five students were questioned about writing on a blackboard. Statements from each imply C wrote it, as two people would be lying in any other case.

1. 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:
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.
Answer: 1 𝑚𝑜𝑣𝑒

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
=
1
2
, therefore area for
∆𝑩𝑪𝑬 =
1
2
∆𝑩𝑪𝑫
∆𝑨𝑩𝑬 =
1
2
∆𝑨𝑩𝑫
∴ ∆𝑨𝑩𝑪 =
1
2
𝒐𝒇 𝒔𝒉𝒂𝒅𝒆𝒅 𝒂𝒓𝒆𝒂 = ______ 𝒄𝒎 𝟐

3. 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 _____
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?

4. 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
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?