![Digit Sum](/sites/default/files/styles/medium/public/thumbnails/content-97-11-six1-icon.jpg?itok=k7f93Lsh)
Place value
![Digit Sum](/sites/default/files/styles/medium/public/thumbnails/content-97-11-six1-icon.jpg?itok=k7f93Lsh)
![Repeaters](/sites/default/files/styles/medium/public/thumbnails/content-97-09-six3-icon.jpg?itok=mpCHzXdH)
problem
Repeaters
Choose any 3 digits and make a 6 digit number by repeating the 3
digits in the same order (e.g. 594594). Explain why whatever digits
you choose the number will always be divisible by 7, 11 and 13.
![2-Digit Square](/sites/default/files/styles/medium/public/thumbnails/content-97-07-six2-icon.jpg?itok=jK3kWII9)
problem
2-Digit Square
A 2-Digit number is squared. When this 2-digit number is reversed
and squared, the difference between the squares is also a square.
What is the 2-digit number?
![Latin Numbers](/sites/default/files/styles/medium/public/thumbnails/content-02-09-15plus4-icon.png?itok=Ui3_Xa50)
![Basic Rhythms](/sites/default/files/styles/medium/public/thumbnails/content-02-06-15plus4-icon.jpg?itok=6yMI9PNc)
![Binary Squares](/sites/default/files/styles/medium/public/thumbnails/content-02-05-15plus2-icon.jpg?itok=UvvW0ax0)
problem
Binary Squares
If a number N is expressed in binary by using only 'ones,' what can
you say about its square (in binary)?
![Novemberish](/sites/default/files/styles/medium/public/thumbnails/content-01-11-15plus1-icon.gif?itok=wX8fMhNB)
problem
Novemberish
a) A four digit number (in base 10) aabb is a perfect square. Discuss ways of systematically finding this number.
(b) Prove that 11^{10}-1 is divisible by 100.
![DOTS Division](/sites/default/files/styles/medium/public/thumbnails/content-01-06-15plus2-icon.jpg?itok=lhIT7p-b)
problem
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}.
![BT.. Eat your heart out](/sites/default/files/styles/medium/public/thumbnails/content-99-09-15plus3-icon.gif?itok=b5WEL3hD)
problem
BT.. Eat your heart out
If the last four digits of my phone number are placed in front of the remaining three you get one more than twice my number! What is it?
![Purr-fection](/sites/default/files/styles/medium/public/thumbnails/content-99-01-15plus1-icon.jpg?itok=UdOa836I)