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Puzzles

8 December

Noel writes the numbers 1 to 17 in a row. Underneath, he writes the same list without the first and last numbers, then continues this until he writes a row containing just one number:
What is the sum of all the numbers that Noel has written?

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Tags: numbers

6 December

There are 5 ways to tile a 4×2 rectangle with 2×1 pieces:
How many ways are there to tile a 12×2 rectangle with 2×1 pieces?

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5 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.
++= 15
+ +
++= 15
+ × ÷
++= 15
=
15
=
15
=
15

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Tags: numbers, grids

4 December

If \(n\) is 1, 2, 4, or 6 then \((n!-3)/(n-3)\) is an integer. The largest of these numbers is 6.
What is the largest possible value of \(n\) for which \((n!-123)/(n-123)\) is an integer?

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3 December

190 is the smallest multiple of 10 whose digits add up to 10.
What is the smallest multiple of 15 whose digits add up to 15?

2 December

Holly adds up the first six even numbers, then adds on half of the next even number. Her total is 49.
Next, Holly adds up the first \(n\) even numbers then adds on half of the next even number. This time, her total is 465124. What is \(n\)?

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23 December

How many numbers are there between 100 and 1000 that contain no 0, 1, 2, 3, or 4?

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22 December

Ivy makes a sequence by starting with the number 35, then repeatedly making the next term by reversing the digits of the current number and adding 6. The first few terms of this sequence are:
$$35$$ $$53+6 = 59$$ $$95+6 = 101$$
What is the first number in Ivy's sequence that is smaller than the previous term?

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Tags: numbers

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