快猫短视频

#183 Animal rights

set by Zoe Mensch

Hattie keeps an old animal encyclopaedia on her shelf that comes in three volumes, each roughly 5 centimetres thick. The first volume has all the animals arranged alphabetically from A to F, the second from G to O and the third from P to Z.

Hattie has bookmarked six of her favourite animals: the aardvark, fruit bat, gecko, oyster, pangolin and zonkey, with the bookmarks sticking out of the top of the volumes as shown above. At least, that is how they looked until her granddaughter shuffled the order of the books. Now, the bookmarks between the aardvark and gecko are further apart than the ones between the fruit bat and pangolin, but not as far apart as the zonkey and oyster bookmarks.

As Hattie looks at the books on the shelf, the oyster bookmark is still to the right of the aardvark. 鈥淚mpossible,鈥� you say? Not at all. In what order are the books now arranged?

Solution next week

#182 Riff raffle

Solution

Each strip contained the same number of tickets. Palindromic numbers are of the form ABBA, and if you experiment with a few such numbers (e.g. 1661, 8228 and 5775), you will find they are always divisible by 11.

This is because ABBA in longhand is 1000A + 100B + 10B + A, which can be simplified to 1001A + 110B, which equals 11 脳 (91A + 10B). Since 1001 is itself a multiple of 11, the tickets must have been sold in strips of 11, with the winning tickets always being the first one in the strip.