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The Games' Medals

Stage: 1 Challenge Level: Challenge Level:2 Challenge Level:2

We had a good number of ideas sent in for this challenge. New City school London pupils by the names of Patrick, William, Hilin, Jhumana, Anika, Sascha, Rizwan, Joe, Zainab, Aqsa, Bianca, Teddy, Kyra, Shakir, Arif and Hamza all sent in good solutions. Well done all of you! Jiang from the Gardeb International School School in Malaysia sent in the following (their own capital letters)

 

FIRSTLY,Afzal WOULD LIKE TO GET A GOL MEDAL, SO THE TWO WAYS THAT HE COULD
GET IT IS,

(1.)AFZAL GETS A GOLD,Bengy GETS A SILVER and Chrissy GETS A BRONZE.  2.)AFZAL GETS GOLD, CHRISSY GETS SILVER AND BENGY GETS BRONZE.) SECONDLY, IF BENGY WOULD LIKE TO GET A GOLD MEDAL, THERE ARE TWO WAYS HE COULD GET IT, (1.) BENGY GETS A GOLD, AFZAL GETS A SILVER AND CHRISSY GETS A BRONZE. 2.)BENGY GETS A GOLD, CHRISSY GETS A SILVER AND AFZAL GETS A BRONZE.) THIRDLY, IF CHRISSY WOULD LIKE TO GET A GOLD MEDAL, THERE ARE TWO WAYS HE COULD GET IT,( 1.) CHRISSY GETS A GOLD, AFZAL GETS A SILVER AND BENGY GETS A BRONZE. 3.) CHRISSY GETS A GOLD, BENGY GETS A SILVER AND AFZAL GETS A BRONZE.) OVERALL THERE ARE 6 WAYS THAT EACH OF THEM CAN GET A GOLD MEDAL. I CHOOSE THIS WAY TO SOLVE THIS PROBLEM, BECAUSE BY LISTING EACH WAY ONE BY ONE THE DIFFERENT WAYS THAT A PERSON CAN WIN A GOLD MEDAL, IT IS MUCH EASIER AND CLEARER TO SOLVE.

Another explanation of an idea came from Tanya at Northowram Primary School in which she says;

 

It says find how many ways of winning is there i found the answer of $6$ ways to win. My aproach: systematically order first all the ways of a winning a,b,c and a,c,b
then all the ways of b winning b,c,a and b,a,c
lastly all the ways of c winning c,b,a and c,a,b

add all the methods together and you get $6$ ways to do it.

 

We also had good answers from Denika at ACS School in Egham, Mapalo from Sacred Heart School, James and Ben from Milton Rd School, here in Cambridge. Jamal and Holly and Gea sent in solutions but we do not know where from.  Well done all of you, you showed such interest.