快猫短视频

#244 Wheel-to-reel

Set by Zoe Mensch

Jim Ford and his daughter Jade were leaving the Old Hat Cinema Club after watching the classic silent western Sunset At Cactus Rock.

鈥淲hat did you think?鈥� asked Jim. 鈥淚t was alright,鈥� said Jade, 鈥渂ut the CGI wasn鈥檛 great. At the end, when the stagecoach was at top speed, none of the wheels were moving!鈥�

鈥淎h,鈥� smiled Jim. 鈥淭hat鈥檚 because those old movies were filmed at 16 frames per second.鈥� Jade鈥檚 eyes glazed over as her dad launched into more western nerdery. 鈥淭hose coaches were called 鈥榝our-yarders鈥� because the circumference of the back wheels was 4 yards.鈥�

鈥淎 yard?鈥� asked Jade. 鈥淚t鈥檚 an old measure, a bit shorter than a metre,鈥� said her father. 鈥淭he back wheels had 24 spokes. The front wheels had 12 spokes and were three-quarters the diameter of the back wheels. On those dirt roads, they weren鈥檛 very quick 鈥� Usain Bolt could have run faster.鈥�

How fast, in old-fashioned yards per second, was the stagecoach moving when its wheels appeared to be stationary?

Solution next week

#243 Emmental arithmetic

Solution

For two three-digit numbers to clash, they must only contain digits that are still valid when a ticket is turned upside down. 0, 1, 2, 5 and 8 all read the same in this case, while 6 becomes 9 and vice versa.

To get two numbers that are very close, the hundreds digit needs to be the same or at most different by 1. Differing by 1 could give us numbers such as 081 and 180 which differ by 99. We can do better by using a 9 in the middle for 091 and 160, differing by just 69. But the closest match is by making the hundreds digit and the units digit the same and using a 6 or 9 in the middle, such as 868 and 898, giving a difference of 30. As long as there are fewer than 31 customers at a time, there won鈥檛 be a clash.