### 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?

### Summing Consecutive Numbers

Many numbers can be expressed as the sum of two or more consecutive integers. For example, 15=7+8 and 10=1+2+3+4. Can you say which numbers can be expressed in this way?

##### Stage: 3 Challenge Level:

The number $747$ can be formed by adding a $3$-digit number
with its reversal: $621 + 126 = 747$, for example.

Can you find the other two ways of making $747$ in this way?

Which other numbers between $700$ and $800$ can be formed from a number plus its reversal?
There are more than five...

Can you explain how you know you have found all the possible numbers?

How many numbers between $300$ and $400$ can be formed from a number plus its reversal. And between $800$ and $900?$...

The number $1251$ can be formed by adding a $3$-digit number with its reversal.
Which other numbers between $1200$ and $1300$ can be formed from a number plus its reversal? And between $1900$ and $2000?$...

With thanks to Don Steward, whose ideas formed the basis of this problem.