快猫短视频

#182 Riff raffle

Quadrucon is an event that is themed around four-digit numbers, so when the organisers decided to hold a charity raffle, it made sense for all the ticket numbers to have four digits. Tickets were printed in one long roll, beginning with 1001 at the start of the roll and numbered consecutively from there. Tickets were then sold to delegates in strips of a fixed length.

Once everyone had bought a strip of tickets, event organiser Ivy Tetraglyph took to the microphone and announced that the first winning ticket number was 2772.

鈥淭hat鈥檚 a palindrome!鈥� said somebody. And by strange coincidence, it turned out that all the other winning numbers were palindromic too.

As the winners filed forwards to claim their prize of a digital clock, the Quadrucon team noticed an interesting pattern: every winning ticket was the smallest number on the strip it was attached to. In fact that is the only place where palindromic numbers could have been.

What length were the strips of tickets sold in?

Solution next week

#181 A loss for words

Solution

To score precisely 98 per cent with only one loss, Wendy must have lost on her 50th game, giving her a score of 49/50. After another 50 winning games, she will reach 99/100, precisely 99 per cent, but she needs a score of 99.5 per cent to round up to 100 per cent. 99.5 per cent is 199/200, so altogether she needs to win another 150 games in a row.