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# Numbers – The Three Spartans

(5)
Tuition given in the topic of E-Maths Tuition Questions from the desk of at 5:08 pm (Singapore time)

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Nevermind if you are too young to know who the Spartans were. But because they tend to appear (whether as Spartans or not) in your E-Maths Paper 1, so STUDENTS!!! PREPARE YOUR HOMEWORK!!!!!!!!!!!!!

To warn King Leonidas of the approaching Persian army, three Spartan scouts are assigned to send signals from three different posts at 0600 hours everyday. The first Spartan signals every 16 seconds, the second Spartan signals every 40 seconds and the third Spartan signals every 64 seconds.

Find the time, correct to the nearest minute, when the three Spartan scouts signal simultaneously.

HAROOH!!! HAROOH!!! HAROOH!!!

P.S. If thou art still stuck, do climb a mountain and seek the Oracle in the form of Miss Loi’s wise old primary school teacher friend Mdm Lau Chio Min. But please be gentle to her and don’t shout “HAROOH!!!” into her face.

### Revision Exercise

To show that you have understood what Miss Loi just taught you from the centre, you must:

1. fggffggf commented in tuition class

2008
Jun
18
Wed
3:48pm

1

That means I'm going to find the LCM of the 16, 40 and 64, then applying the finding to the actual question.

.'. The LCM is .
320 seconds = 5 minutes and 20 seconds
.'. The time, correct to the nearest minute, when the three Spartan scouts signal simultaneously is 0605 hours.

And putting Math aside, the Spartans movie 笑到我辘地！

2. Miss Loi Friend Miss Loi on Facebook @MissLoi commented in tuition class

2008
Jun
25
Wed
12:48am

2

When you see stuffs happening simultaneously "every x seconds/minutes etc" (being traffic lights flashing, water fountains sprouting, buses arriving, Spartans signaling etc.) in the question and you're being asked to find when they will happen at the same time, you should instantly recognize that you're dealing with LCM!

Another way of looking at and understanding this question for those who may still be unsure:

1st Spartan signals at: 16s, 32s, 48s, 64s, ... multiples of 16
2nd Spartan signals at: 40s, 80s, 120s, 160s, ... multiples of 40
3rd Spartan signals at: 64s, 128s, ... multiples of 64

So the time when all three signals at the same time is the Least Common Multiple of 16, 40 and 64, with detailed workings kindly provided courtesy of fggffggf above 😉

P.S. fggffggf 你係廣東人?

3. Li-sa commented in tuition class

2008
Jun
25
Wed
2:51pm

3

我係香港人，也是會考生。瞧我的繁體中文！

4. Li-sa commented in tuition class

2008
Jun
26
Thu
12:31pm

4

当我是交流生吧，反正香港会考生学的数学和新加坡的差不多，只是没有集合(set)和自然对数(natural logarithm)。但这无所谓，因为我会自动自觉地学习。
不过我住在香港多年才称自己「香港人」。

5. yo commented in tuition class

2009
Nov
10
Tue
10:22am

5

wad is the meaning of lowest common multiple

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