# Puzzles

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The sum of all the numbers in the eighth row of Pascal's triangle.

Clarification: I am starting the counting of rows from 1, not 0. So (1) is the 1st row, (1 1) is the 2nd row, (1 2 1) is the 3rd row, etc.

## 18 December

The smallest number whose sum of digits is 25.

## 17 December

The number of degrees in one internal angle of a regular polygon with 360 sides.

## 16 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 than can be made from the digits in red boxes.

× | × | = 6 | |||

× | × | × | |||

× | × | = 180 | |||

× | × | × | |||

× | × | = 336 | |||

= 32 | = 70 | = 162 |

## 15 December

A book has 386 pages. What do the page numbers on the two middle pages add up to?

## 14 December

In July, I posted the Combining Multiples puzzle.

Today's number is the largest number that cannot be written in the form \(27a+17b\), where \(a\) and \(b\) are positive integers (or 0).

## 13 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 smaller number in a red box to the power of the larger number in a red box.

+ | - | = 8 | |||

- | - | - | |||

+ | ÷ | = 3 | |||

+ | ÷ | × | |||

+ | × | = 120 | |||

= 8 | = 1 | = 8 |

## 12 December

Here is a list of facts about today's number:

- If a×b is a factor of it, with a and b both positive integers, then either a or b is one.
- The sum of its digits is 14.
- It is odd.
- The product of its digits is 36.
- It is a palindrome when written in base 9.
- It is smaller than yesterday's number.
- It is 4 more than a multiple of 5.
- It is two less than a prime number.
- It is the number of a bus stopping at Richmond station.