### Consecutive Numbers

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

### Calendar Capers

Choose any three by three square of dates on a calendar page...

### Days and Dates

Investigate how you can work out what day of the week your birthday will be on next year, and the year after...

# Seven Dwarfs

##### Stage: 3 Short Challenge Level:
Suppose the youngest dwarf is $x$ years old. The sum of the ages of the youngest three is $x+(x+1)+(x+2)=3x+3$, and the sum of the ages of the oldest three is $(x+4)+(x+5)+(x+6)=3x+15$.

We know that $3x+3=42$, so $3x+15=42+12=54$.

This problem is taken from the UKMT Mathematical Challenges.