### Consecutive Numbers

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

### Have You Got It?

Can you explain the strategy for winning this game with any target?

### Counting Factors

Is there an efficient way to work out how many factors a large number has?

# 2014 Even Numbers

##### Age 11 to 14 ShortChallenge Level

Comparing the two sums
Sum of the first 2014 even numbers is $2+4+6+8+10+12+...$
Sum of the first 2014 odd numbers is   $1+3+5+7+\ 9\ +11+...$
Difference is $1+1+1+1+\ 1\ +\ 1\ +...$

There are 2014 terms - so the difference is 2014.

Working it out by considering shorter sums
First 2 evens/odds
2 + 4 = 6
1 + 3 = 4
The difference between 6 and 4 is 2.

First 3 evens/odds
2 + 4 + 6 = 12
1 + 3 + 5 = 9
The difference between 12 and 9 is 3.

First 4 evens/odds
2 + 4 + 6 + 8 = 20
1 + 3 + 5 + 7 = 16
The difference between 20 and 16 is 4.

Assuming the pattern continues, the difference between the sum of the first 2014 even numbers and the sum of the first 2014 odd numbers will be 2014.

You can find more short problems, arranged by curriculum topic, in our short problems collection.