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**NETFLIX: ** the Producers of instant cult TV series “Stranger Things” clearly appreciate the wonder of the number Eleven: they even (or should that be “oddly”) named the series’ main character “Eleven”.

**CUBE NETS: **there are eleven distinct nets of cubes. A **cube net** is a (flat) arrangement of six squares that “fold up” to make a cube. An example is the **hexomino** (six joined squares) on the left, but not the one on the right (in which the two marked squares fight to become the same face of the cube).

**OCTAHEDRON NETS: **rather wonderfully, there are also exactly eleven distinct nets of the octahedron! If you’ve not met one yet, the **Octahedron** is a regular 3D shape with 8 triangular faces (think of it as two square-based pyramids with their square faces glued together). The cube and octahedron are “**dual polyhedra**“: the cube has 6 faces and 8 **vertices **(like 3D “corners”) whereas the octahedron has 8 faces and 6 vertices. They both have 12 edges. If you take a cube (or octahedron), replace each face with a vertex and each vertex with a face, then join the new vertices together, you get an octahedron (or cube). Magic! It’s this “dual” property that means both shapes have the same number of nets: eleven. For the same reason, the regular **Dodecahedron **and **Icosahedron **also have the same number of distinct nets: 43380.

**DIVISIBILITY TEST:** it’s easy to see if a (whole) number is divisible by ten: just see if it ends in a zero. And a multiple of five will always end in 0 or 5. The test for divisibility by 3 is slightly more cunning: you take the **digit sum** e.g. 1062 is divisible by 3 because 1+0+6+2=9, which is divisible by 3, and therefore so is the original 1062.

Rather fabulously, the test for divisibility by eleven is to look at the **alternating digit sum**: just alternately add and subtract consecutive digits, if the result is divisible by 11 then so is the original number e.g. try 92818. We see that 9-2+8-1+8=22, which is divisible by 11, therefore so is 92818 (it’s 11×8438).

**ALL PALINDROMES WITH AN EVEN NUMBER OF DIGITS ARE DIVISIBLE BY 11: ** e.g. 7337=11×667, or 623326=11×56666. Can you see why this is true? (HINT: use the “alternating digit sum” divisibility test).

**SPORTS TEAMS:** there are 11 footballers on each side, and 11 cricketers in a team. Could this perhaps be because 11 is a prime number? A team of, say, ten members might naturally split into two groups of five, harming the team dynamics?

**TIMES TABLE:** finally, of course, eleven is everyone’s favourite **times table**. To multiply a one-digit number by eleven, merely repeat that digit e.g. 11×5=55. To multiply a 2-digit number by 11 is only marginally harder: pull the two digits apart and put their sum in the middle e.g. 11×53=583 (since 5+3=8).

This sometimes involves a “carry” e.g. 11×68=748 because 6+8=14 so in the hundreds column the 6 becomes 7.

**MULTIPLYING A LONGER NUMBER BY ELEVEN:** this is a “**magic trick**” that never fails to impress! Simply start at the units end, and add successive digits, placing the sum in between, like this:

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