Singapore PSLE Math baffled Anxious Parents

One afternoon 5 friends rented 3 bikes from 5 p.m. to 6:30 p.m. and took turns to ride on them. At any time, 3 of them cycled while the other 2 friends rested.

If each of them had the same amount of cycling time, how many minutes did each person ride on a bike?

Note: PSLE (Primary Schools Leaving Exams) is the Singapore National Exams for all 12 year-old pupils at Primary 6 year end. The result of which will determine which secondary school the pupil is qualified to enter the following year. Math subject, besides Science, English and mother tongue (Chinese or Malay or Tamil) are tested in PSLE.

[Answer] Try before you scroll down below ….

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Answer = each student rides 18 mins per bike (= 90 mins /5 ).

The “3” bikes are tricky “smokes” not relevant, it could be any “n” (<6) bikes , as long as total 90 mins, and each student rides same duration.

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World Cup Math Analysis : Korea vs Germany (2:0)

World Cup 2018

Surprising Result:

World No.1 (Germany) Lost to World No.59 (Korea) – why ?

Reason: Math !

For weak Korea to win, the best strategy is to keep the goal number as low as possible with strongest defence.

Conclusion: Highest chance for Korea to beat Germany is either 1 or 2 goals !

Germany lost by not launching a strong attack to score as many goals as possible.

Note : 2017 International Math Olympiad (IMO) World Champion Team was Korea.

The actual Game proved the Korean “Math” strategy was right: (2:0)

Boolean Algebra

George Boole [2/11/ 1815 – 8/12/ 1864]: 《The Laws of Thought》: symbolic logic representation of thought.

Let x = class of sheep’s

y = white

=> white sheep = xy = yx = sheep white

then Commutativity Law:

\boxed {xy = yx}

Let x= rivers, y = estuaries河口, z= navigable 通航

then, Associativity Law:

\boxed {(xy)z= x(yz)}

A sheep is a sheep,

\boxed {xx = x^{2} = x}

Note: x = 0 or 1 fulfills the above equation.

If x = class of men

y = class of women

z = class of adults (either men or women)

\boxed {z = x + y}

w = European

then Distributive Law:

\boxed {w(x+y) = wx + wy}

If t = Chinese

then all non-Chinese men = {x – t}

If s = Singaporean,

then

\boxed {s(x - t ) = sx - st}