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Click here to win prizes by solving the mscroggs.co.uk puzzle Advent calendar.
Click here to win prizes by solving the mscroggs.co.uk puzzle Advent calendar.

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Puzzles

3 December

If you write out the numbers from 1 to 1000 (inclusive), how many times will you write the digit 0?

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2 December

The number \(7n\) has 37 factors (including 1 and the number itself). How many factors does \(8n\) have?
There was a typo in this puzzle. It originally read "38 factors" when it was meant to say "37 factors".

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1 December

The geometric mean of a set of \(n\) numbers can be computed by multiplying together all the numbers then computing the \(n\)th root of the result.
The factors of 4 are 1, 2 and 4. The geometric mean of these is 2.
The factors of 6 are 1, 2, 3, and 6. The geometric mean of these is \(\sqrt{6}\).
The geometric mean of all the factors of today's number is 22.

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24 December

There are six ways to put two tokens in a 3 by 3 grid so that the diagonal from the top left to the bottom right is a line of symmetry:
Today's number is the number of ways of placing two tokens in a 29 by 29 grid so that the diagonal from the top left to the bottom right is a line of symmetry.

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23 December

198 is the smallest number that is equal to 11 times the sum of its digits.
Today's number is the smallest number that is equal to 48 times the sum of its digits.

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22 December

Put the digits 1 to 9 (using each digit exactly once) in the boxes so that the sums are correct. The sums should be read left to right and top to bottom ignoring the usual order of operations. For example, 4+3×2 is 14, not 10. Today's number is the largest number you can make with the digits in the red boxes.
++= 18
+ + +
÷-= 1/2
+ + +
+÷= 3/2
=
24
=
8
=
13

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Tags: numbers, grids

21 December

There are 3 ways to order the numbers 1 to 3 so that no number immediately follows the number one less that itself:
Today's number is the number of ways to order the numbers 1 to 6 so that no number immediately follows the number one less that itself.

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20 December

18 can be written as the sum of 3 consecutive (strictly) positive integers: 5 + 6 + 7.
18 can also be written as the sum of 4 consecutive (strictly) positive integers: 3 + 4 + 5 + 6.
18 is in fact the smallest number that can be written as the sum of both 3 and 4 consecutive (strictly) positive integers.
Today's number is the smallest number that can be written as the sum of both 12 and 13 consecutive (strictly) positive integers.

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Tags: numbers, sums

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