Fatimah and Hairu play Congkak (Math Question)


Fatimah is a lower primary school student. She is cheerful and full of energy. Besides going to school and doing her school works, she is spends time with her brothers on games and activities. She learned a new game call Congkak just two weeks ago. She likes the game very much and she always challenges Hairu, her brother on the game. 

Congkak is a traditional Malay game. It is a popular board game in the South East Asian region and believed to have been originated from Malacca. It used to be a game for women. They played the game with holes dug on the sand field and using small pebbles as seeds.


Today, it has been developed to become a board game and using marbles (98 pieces) as seeds. It requires at least two to play the game and more men are showing interest in participating in the game too. The board is of a shape of ship and usually make of wood with various in size and decoration in design. It has 14 holes, 7 holes on each side, and a large hole on each end of the board which used as a storage place for each player. The mission of the players is to collect more seeds than your opponent, by moving the seeds on one’s side of the board. In order to win, players need to strategize their moves and to calculate the number of seeds needed to be moved each time to avoid more seeds ending up at the opponent’s side. 

Fatimah and Hairu bring out the marbles and prepare to start the game. 

Upper primary school mathematics question UPQ3

 20% of the number of marbles Fatimah had is equal to the 35% of the number Hairu had. After Fatimah given away 30 marbles and Hairu collected 20 marbles, 30% of the number of marbles Fatimah had is equal to the 50% of the number Hairu had. What is the number of marbles each of them had at first?


Assume:  Fatimah had X number of marbles and Hairu had Y number of marbles at first.

20% of the number of marbles Fatimah had is equal to the 35% of the number Hairu had at first

Now Fatimah given away 30 marbles and Hairu collected 20 marbles and the ratio changed.

                   30% of  (X – 30) = 50% of (Y +20) or 30(X-30) = 50(Y+20)

                              30X – 900 = 50Y + 1000

                                             3X = 5Y +190

                                 21Y – 20Y     = 190*4  

        Y     = 760    (Number of marbles Hairu originally has)

        X    = 1330   (Number of marbles Fatimah originally has)                         

 Or, using model

X (20 + 20 + 120/7) = (40 + 120/7) X = 100Y        equation 1


60(X – 30) = 100(Y + 20) = 100Y + 2000               equation 2

Solve the two equations,

60X – 1800 = (40 + 120/7) X + 2000

20X – (120/7)X = 3800

140X – 120X = 3800*7

20X = 3800*7

    X = 190*7 = 1330      (Number of marbles Fatimah originally has)

100Y = 40*1330 + 120*1330/7

       Y = 760 (Number of marbles Hairu originally has)

They have more than enough marbles to play a game of Congkak. 

8 responses »

  1. Interesting post and you are absolutely right that congkak is a Southeast Asian traditional game and in fact there is a close variant of the congkak from Sri Lanka called chonka. It is true that congkak is mostly played by girls and this game encourages the players to mentally calculate and strategise.

    • Oh. I hv not know about the similar game that from Sri Lanka. Let me do some reserach and bring them in to my blog when I am ready. By the way, I generate this blog with two aims. One of them is to assist student and parents event tuitors on Singapore primary school mathematics. Another aims is to able to share some traditionals, culture of South East Asia. I hope that I can make the blog reading interesting and enjoyable. Do few free to give me feedbacks and suggestions. Thanks!

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