### 14 Divisors

What is the smallest number with exactly 14 divisors?

### 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?

### Helen's Conjecture

Helen made the conjecture that "every multiple of six has more factors than the two numbers either side of it". Is this conjecture true?

# Magic Letters

##### Stage: 3 Challenge Level:

Charlie has made a Magic V with five consecutive numbers:

It is a Magic V because each 'arm' has the same total.

Alison drew this magic V:

Charlie said "That's really just the same Magic V as mine!"

What do you think Charlie meant?

Click below to see the other Magic Vs that Charlie considers to be the same as his:

Can you find other Magic Vs using the numbers $1$ to $5$ that are different from Charlie's?

How will you know when you have found all the different Magic Vs using the numbers $1$ to $5$?

What happens if you use the numbers from $2$ to $6$?

From $3$ to $7$? $\dots$

You can use this spreadsheet to investigate Magic Vs made from any five consecutive numbers.

Try to find a strategy to find efficiently all Magic Vs and their totals for any given set of numbers.

Can you describe how to find the possible Magic Vs using the numbers $987, 988, 989, 990, 991$?

Can you describe an efficient strategy for finding a Magic V where each arm has a total of 1000?

Charlie and Alison drew some more magic letters.

 A Magic L A Magic N A Magic W

Investigate some of these Magic Letters in the same way that you explored Magic Vs. What general conclusions can you reach? You can use this spreadsheet to explore.