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Triangle Incircle Iteration

Keep constructing triangles in the incircle of the previous triangle. What happens?

Vedic Sutra - All from 9 and Last from 10

Vedic Sutra is one of many ancient Indian sutras which involves a cross subtraction method. Can you give a good explanation of WHY it works?

Funny Factorisation

Using the digits 1 to 9, the number 4396 can be written as the product of two numbers. Can you find the factors?

Zeller's Birthday

Age 14 to 16 Challenge Level:

What day of the week were you born on? Do you know?

Here's a way to find out.

For example, if your date of birth was 6 July 1989 :

$D = 6$ , $M = 7$ , and $Y = 1989$

If $M$ had been a 1 or 2, subtract 1 from $Y$ and add 12 to $M$.

$Y_F$ is made from the first two digits of $Y$ and $Y_L$ is made from the last two digits of $Y$.

To begin, work out the sum of all the integer parts of $2.6M - 5.39$ , of $\frac{Y_F}{4}$ , and of $\frac{Y_L}{4}$

Add $D$ and $Y_L$ into that total, and then subtract 2 lots of $Y_F$

Divide that final answer by 7 and notice the remainder .

A remainder value of 0 means the date was a Sunday, 1 means it was a Monday, 2 for a Tuesday, and so on.

Can you follow the method (what you actually have to do) ?

You could check some dates you happen to know the answer for ?

When you are getting good at using the method start to ask yourself how it works and why does it give the right result?

Why 2.6 and why 5.39?