快猫短视频

#220 Artificial Intelli-Vision song contest

Set by Zoe Mensch

There was controversy at this year鈥檚 Artificial Intelli-Vision song contest, in which each of the competing countries used AI to generate their entries.

Every nation had a judging panel that gave a score to each of the others. The 鈥渟ongwriters鈥� all tried to engineer a higher score for their country by letting an AI generate their ditty as a danceable blend of one other country鈥檚 all-time favourite tunes.

This led to a strange outcome. Each judging panel awarded 10 points to the song tailored to its national preferences and the same lower number of points to all of the others. For example, the Transylvania panel gave a perfect 10 to Ruritania鈥檚 artificially intelligent effort Everybody Let鈥檚 Dance Last Night Tonight, while giving only a 7 to all the rest.

The song contest鈥檚 board decided to restore artistic integrity to this prestigious event by deducting the inflated 10 from each country鈥檚 set of scores. After this, the grand total of all scores was 222, with no two nations tied for any position. Can you figure out how many countries took part and how many points the winning song scored?

Solution next week

#219 The second red queen

Solution

To maximise my chances of picking the second red queen, I should nominate the bottom card in the pack of 52. Working out the chance of the second queen鈥檚 location is quite hard, so look instead at the chance of the first red queen being in particular positions. The chance that the first red queen is top of the pack is 2/52, or about 3.85 per cent. The chance that it is second is slightly lower, the chance it is third lower still, and this continues to the bottom card, which has a zero chance of being the 鈥渇irst鈥� red queen. Now, turn the pack upside down. What was the 鈥渇irst鈥� red queen is now the 鈥渟econd鈥� red queen, So, by symmetry, the most likely position for the second red queen is the bottom of the pack.