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# Puzzles

## 5 December

I make a book by taking 111 sheets of paper, folding them all in half, then stapling them all together through the fold. I then number the pages from 1 to 444.
Today's number is the sum of the two page numbers on the centre spread of my book.
Tags: numbers, books

## 4 December

Today's number is the number of 0s that 611! (611×610×...×2×1) ends in.

## 3 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 numbers in the red boxes.
 + + = 11 - + × + - = 11 - - - + + = 11 =-11 =11 =11
Tags: numbers, grids

## 1 December

There are 5 ways to write 4 as the sum of 1s and 2s:
• 1+1+1+1
• 2+1+1
• 1+2+1
• 1+1+2
• 2+2
Today's number is the number of ways you can write 12 as the sum of 1s and 2s.
Tags: numbers

## Square and cube endings

Source: UKMT 2011 Senior Kangaroo
How many positive two-digit numbers are there whose square and cube both end in the same digit?

## Digitless factor

Ted thinks of a three-digit number. He removes one of its digits to make a two-digit number.
Ted notices that his three-digit number is exactly 37 times his two-digit number. What was Ted's three-digit number?

## Backwards fours

If A, B, C, D and E are all unique digits, what values would work with the following equation?
$$ABCCDE\times 4 = EDCCBA$$

## Cube multiples

Six different (strictly) positive integers are written on the faces of a cube. The sum of the numbers on any two adjacent faces is a multiple of 6.
What is the smallest possible sum of the six numbers?

## Archive

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