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# Puzzles

## Archive

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## 24 December

Today's number is the smallest number with exactly 28 factors (including 1 and the number itself as factors).

## 23 December

In the song The Twelve Days of Christmas, how many presents have been given after 8 days?

## 21 December

The factors of 6 (excluding 6 itself) are 1, 2 and 3. $$1+2+3=6$$, so 6 is a perfect number.
Today's number is the only three digit perfect number.

## 20 December

What is the largest number that cannot be written in the form $$10a+27b$$, where $$a$$ and $$b$$ are nonnegative integers (ie $$a$$ and $$b$$ can be 0, 1, 2, 3, ...)?

## 19 December

Put the digits 1 to 9 (using each digit exactly once) in the boxes so that the products are correct. Today's number is the smallest number that can be made using the digits in the red boxes.
 × × = 90 × × × × × = 84 × × × × × = 48 =64 =90 =63
Tags: numbers, grids

## 18 December

Today's number is the maximum number of pieces that a (circular) pancake can be cut into with 17 straight cuts.

## 17 December

Arrange the digits 1-9 in a 3×3 square so that every row makes a three-digit square number, the first column makes a multiple of 7 and the second column makes a multiple of 4. The number in the third column is today's number.
 square square square multiple of 7 multiple of 4 today's number
Tags: numbers, grids

## 15 December

The string ABBAABBBBB is 10 characters long, contains only A and B, and contains at least three As.
Today's number is the number of different 10 character strings of As and Bs that have at least three As.
Tags: numbers