### Archive

Archive for the ‘Extension’ Category

## Happy New Year

### Happy New Leap Year

2012 is a leap year, i.e. it has 366 days. 366 can be written as the sum of consecutive square numbers:
366 = 82 + 92 + 102 + 112

Non-leap years have 365 days. 365 can be written as the sum of consecutive squares in two different ways:
365 = 102 + 112 + 122
365 = 132 + 142

Neither 366 nor 365 are square numbers themselves. Are there any square numbers that can be written as the sum of consecutive squares?

Happy new year

Categories: Extension Tags: , , , ,

## Pythagoras extension

### How odd is Pythagoras?

Pythagorean triples are sets of positive integers (a,b,c) where a2+b2=c2. A Pythagorean triple is primitive if there isn’t a common factor that divides a, b and c.

(3,4,5) and (5,12,13) are primitive Pythagorean triples but (6,8,10) is not as 2 divides 6,8 and 10.

• Is the smallest number in a primitive Pythagorean triple always odd?
• Is the largest number in a primitive Pythagorean triple always odd?

Pythagoras extension

Categories: Extension Tags: ,

## Chocolate puzzle AGT

A Shop sells chocolates at £1 each.

You can exchange 3 wrappers for 1 chocolate.

If you have £45, how many chocolates can you get in total?

Chocolate

Categories: Extension Tags: , ,

## Division extension

Take the number 523523.

• Divide it by 13
• Divide that answer by 11
• What did you get?

Repeat for 791791.

Can you predict numbers it will work for?

The most important question… why?

Division extension

Categories: Extension Tags: ,

## Money – Extension

Money Extension

A man pays £200 into a bank that pays 5% interest per annum.

• How much money will he have in the account after one year?
• two years?
• three years?
• ten years?
• How many years will it take for him to have £10,000?

Watch this interesting video