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Puzzles

17 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.
++= 10
+ × ×
++= 12
+ +
++= 23
=
10
=
12
=
23

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Tags: numbers, grids

16 December

Noel writes the integers from 1 to 1000 in a large triangle like this:
The rightmost number in the row containing the number 6 is 9. What is the rightmost number in the row containing the number 300?

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Tags: numbers

15 December

There are 3 even numbers between 3 and 9.
What is the only odd number \(n\) such that there are \(n\) even numbers between \(n\) and 729?

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14 December

Holly draws a line of connected regular pentagons like this:
She continues the pattern until she has drawn 204 pentagons. The perimeter of each pentagon is 5. What is the perimeter of her line of pentagons?

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Tags: pentagons

13 December

Today's number is given in this crossnumber. The across clues are given as normal, but the down clues are given in a random order: you must work out which clue goes with each down entry and solve the crossnumber to find today's number. No number in the completed grid starts with 0.

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12 December

The determinant of the 2 by 2 matrix \(\begin{pmatrix}a&b\\c&d\end{pmatrix}\) is \(ad-bc\).
If a 2 by 2 matrix's entries are all in the set \(\{1, 2, 3\}\), the largest possible deteminant of this matrix is 8.
What is the largest possible determinant of a 2 by 2 matrix whose entries are all in the set \(\{1, 2, 3, ..., 12\}\)?

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11 December

There are five 3-digit numbers whose digits are all either 1 or 2 and who do not contain two 2s in a row: 111, 112, 121, 211, and 212.
How many 14-digit numbers are there whose digits are all either 1 or 2 and who do not contain two 2s in a row?

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10 December

A line is tangent to a curve if the line touches the curve at exactly one point.
The line \(y=-160\,000\) is tangent to the parabola \(y=x^2-ax\). What is \(a\)?

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