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
true?

Mini-max

Age 11 to 14 Challenge Level:

Consider all two digit numbers ($10$, $11$, . . . ,$99$). In
writing down all these numbers, which digits occur least often, and
which occur most often ?

What about three digit numbers, four digit numbers and so
on?