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Pair Sums

Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?

2014 Even Numbers

Age 11 to 14 Short Challenge Level:

Answer: 2014


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.