快猫短视频

#151 Alien fingers

When the aliens landed in my back garden, my first thought was that they use the same number system as we do, because there was a two-digit number written in our Earthly digits on the side of their spaceship.

But when the aliens emerged from the ship, I saw that they each had 16 fingers. I intuited that they therefore used a hexadecimal (base 16) method of counting. Their first ten digits, from 0 to 9, work just like our terrestrial decimal system, but 10-15 are expressed as A to F, respectively. After F (our 15) comes 10 (our 16), 11 (our 17) and so on. What can I say, I am very intuitive.

In hexadecimal, 1E is the same as our decimal 30 (one 16 and fourteen 1s) and their 25 is our 37 (two 16s and five 1s).

The number painted on the side of their ship was therefore written in hexadecimal. Yet by a remarkable coincidence, it could be translated into our number system by simply reversing the order of the digits.

What was the alien number in Earthly notation?

#150 A jigsaw puzzle

Solution

Conventional jigsaws are rectangular, and multiplying together the number of pieces along the short and long edges gives the total number of pieces. This jigsaw has 468 pieces. The prime factors of 468 are 2, 2, 3, 3 and 13, so possible dimensions of the jigsaw are 26 x 18 or 36 x 13 or 39 x 12, and so on. But conventional jigsaws aren鈥檛 long and thin, so 26 x 18 is the only jigsaw-shaped rectangle. This would have 2 x 26 plus 2 x 16 (not 18, to avoid counting the corner pieces twice) = 84 edge pieces, including corners.