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# Puzzles

## 17 December

Eve picks a three digit number then reverses its digits to make a second number. The second number is larger than her original number.
Eve adds her two numbers together; the result is 584. What was Eve's original number?

## 16 December

Arrange the digits 1-9 in a 3×3 square so that: the median number in the first row is 6; the median number in the second row is 3; the mean of the numbers in the third row is 4; the mean of the numbers in the second column is 7; the range of the numbers in the third column is 2, The 3-digit number in the first column is today's number.
 median 6 median 3 mean 4 today's number mean 7 range 2

## 15 December

There are 5 ways to make 30 by multiplying positive integers (including the trivial way):
• 30
• 2×15
• 3×10
• 5×6
• 2×3×5
Today's number is the number of ways of making 30030 by multiplying.

## 14 December

During one day, a digital clock shows times from 00:00 to 23:59. How many times during the day do the four digits shown on the clock add up to 14?

## 13 December

Each clue in this crossnumber (except 5A) gives a property of that answer that is true of no other answer. For example: 7A is a multiple of 13; but 1A, 3A, 5A, 1D, 2D, 4D, and 6D are all not multiples of 13. No number starts with 0.

## 12 December

For a general election, the Advent isles are split into 650 constituencies. In each constituency, exactly 99 people vote: everyone votes for one of the two main parties: the Rum party or the Land party. The party that receives the most votes in each constituency gets an MAP (Member of Advent Parliament) elected to parliament to represent that constituency.
In this year's election, exactly half of the 64350 total voters voted for the Rum party. What is the largest number of MAPs that the Rum party could have?

## 11 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 product of the red digits.
 + ÷ = 2 + ÷ ÷ ÷ ÷ = 3 ÷ - ÷ ÷ ÷ = 1 =2 =1 =1
Tags: grids, numbers

## 10 December

For all values of $$x$$, the function $$f(x)=ax+b$$ satisfies
$$8x-8-x^2\leqslant f(x)\leqslant x^2.$$
What is $$f(65)$$?
Edit: The left-hand quadratic originally said $$8-8x-x^2$$. This was a typo and has now been corrected.

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