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N000ughty Thoughts

How many noughts are at the end of these giant numbers?

DOTS Division

Take any pair of two digit numbers x=ab and y=cd where, without loss of generality, ab > cd . Form two 4 digit numbers r=abcd and s=cdab and calculate: {r^2 - s^2} /{x^2 - y^2}.

Mod 3

Prove that if a^2+b^2 is a multiple of 3 then both a and b are multiples of 3.

Indivisible

Age 14 to 16 Short
Challenge Level

Answer: 59


Lining up in rows of 3:
 


Lining up in rows of each number:
 


What comes next in each pattern?
 


Next number is a multiple of 3, 4, 5, 6
Lowest common multiples of 3, 4, 5, 6: 60, 120, 180, etc.
Fewer than 100 students $\therefore$ there are 59 students.

 
 
This problem is taken from the UKMT Mathematical Challenges.
You can find more short problems, arranged by curriculum topic, in our short problems collection.