maths recreation

1. The trick is the ruler is 13cm long, i.e. we can measure 2cm length between the 11cm mark and the end of the ruler. Hence, the length of 1cm, 4cm, 5cm and 11cm is easy to obtain under usual measuration method.

2cm can be obtained between 11cm and the right-most end.
3cm can be obtained between 1cm mark and 4cm mark.
6cm can be obtained between 5cm mark and 11cm mark.
7cm can be obtained between 4cm mark and 11cm mark.
8cm can be obtained between 5cm mark and right-most end.
9cm can be obtained between 4cm mark and right-most end.
10cm can be obtained between 1cm mark and 11cm mark.
12cm can be obtained between 1cm mark and right-most end.
13cm can be obtained by the length of the ruler.


2. Five cats can catch five mice in five minutes means that 5 cats can catch 1 mouse in average in one min. Hence, they can catch 100 mices in average in 100 mins.


3. Use four matches each to construct a square. Then we have 2 squares. Put the 2 squares together with rotating one of them by say 45 deg about the centre, then we have a 16-concaved-polygon with two large squares and 8 small right-angled triangle surrounded.


4. Let x be the age of grandson, then 2x is the age of son, 4x is the age of father, and 8x is the age of grandfather.

We then have x + 2x + 4x + 8x = 105, which is easy to know that x = 7. And you can manage to have the ages of all 4 dogs.