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Puzzles

19 December

Today's number is the number of 6-dimensional sides on a 8-dimensional hypercube.

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Tags: 3d shapes

18 December

There are 6 terms in the expansion of \((x+y+z)^2\):
$$(x+y+z)^2=x^2+y^2+z^2+2xy+2yz+2xz$$
Today's number is number of terms in the expansion of \((x+y+z)^{16}\).

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Tags: algebra

17 December

For \(x\) and \(y\) between 1 and 9 (including 1 and 9), I write a number at the co-ordinate \((x,y)\): if \(x\lt y\), I write \(x\); if not, I write \(y\).
Today's number is the sum of the 81 numbers that I have written.

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Tags: numbers

16 December

Arrange the digits 1-9 in a 3×3 square so that the first row makes a triangle number, the second row's digits are all even, the third row's digits are all odd; the first column makes a square number, and the second column makes a cube number. The number in the third column is today's number.
triangle
all digits even
all digits odd
squarecubetoday's number

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Tags: numbers, grids

15 December

Today's number is smallest three digit palindrome whose digits are all non-zero, and that is not divisible by any of its digits.

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14 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
÷ + ÷
÷+= 3
+ - ÷
+×= 33
=
7
=
3
=
3

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Tags: numbers, grids

13 December

There is a row of 1000 lockers numbered from 1 to 1000. Locker 1 is closed and locked and the rest are open.
A queue of people each do the following (until all the lockers are closed):
Today's number is the number of lockers that are locked at the end of the process.
Note: closed and locked are different states.

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12 December

These three vertices form a right angled triangle.
There are 2600 different ways to pick three vertices of a regular 26-sided shape. Sometime the three vertices you pick form a right angled triangle.
Today's number is the number of different ways to pick three vertices of a regular 26-sided shape so that the three vertices make a right angled triangle.

 

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