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Counting Factors

Is there an efficient way to work out how many factors a large number has?

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Summing Consecutive Numbers

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

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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?

Alphabet Soup

Age 11 to 14 Challenge Level:

This challenge is to make up YOUR OWN word-arithmetic challenge.

Each letter represents a digit and where the same letter appears more than once it must represent the same digit each time.

The hard part is to make up some message rather than just using any old letters. Send in your word-arithmetic challenge, together with at least one solution to it.

Another challenge is to discover if the puzzle has just one solution or many. Here are two easy examples; they are just addition sums and you may be more inventive and make up subtractions, multiplications or divisions:

  N R I C H
+ S T A R S
  M A T H S
  M A T H
+ E M A T
  I C A L

Lastly, can you prove that

  N R I C H
+ M A T H S
  S T A R S

cannot be made to work?