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Puzzles

10 December

Put the digits 1 to 9 (using each digit exactly once) in the boxes so that the sums are correct. Today's number is the largest number you can make using the digits in the red boxes.
++= 20
+ + +
++= 10
+ + +
++= 15
=
7
=
23
=
15

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Tags: numbers, grids

9 December

Eve writes down a sequence of consecutive positive integers (she writes more than one number). The sum of the numbers Eve has written down is 844.
Today's number is the smallest integer that Eve has written down.

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8 December

The sum of three integers is 51. The product of the same three integers is 836. What is the product of largest integer and the second-largest integer?

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6 December

When 12345 is divided by today's number, the remainder is 205. When 6789 is divided by today's number, the remainder is 112.

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4 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.
+-= 5
÷ × ×
+-= 5
- ÷ ÷
+×= 10
=
-6
=
18
=
35

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Tags: numbers, grids

3 December

If you write out the numbers from 1 to 1000 (inclusive), how many times will you write the digit 0?

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2 December

The number \(7n\) has 37 factors (including 1 and the number itself). How many factors does \(8n\) have?
There was a typo in this puzzle. It originally read "38 factors" when it was meant to say "37 factors".

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1 December

The geometric mean of a set of \(n\) numbers can be computed by multiplying together all the numbers then computing the \(n\)th root of the result.
The factors of 4 are 1, 2 and 4. The geometric mean of these is 2.
The factors of 6 are 1, 2, 3, and 6. The geometric mean of these is \(\sqrt{6}\).
The geometric mean of all the factors of today's number is 22.

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