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Puzzles

16 December

Some numbers can be written as the sum of two or more consecutive positive integers, for example:
$$7=3+4$$ $$18=5+6+7$$
Some numbers (for example 4) cannot be written as the sum of two or more consecutive positive integers. What is the smallest three-digit number that cannot be written as the sum of two or more consecutive positive integers?

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9 December

Eve writes down a sequence of consecutive positive integers (she writes more than one number). The sum of the numbers Eve has written down is 844.
Today's number is the smallest integer that Eve has written down.

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