What is the smallest number with exactly 14 divisors?
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 made the conjecture that "every multiple of six has more
factors than the two numbers either side of it". Is this conjecture
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.
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.
Click here for a poster version of the Magic Vs.