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#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.

“What did you think?” asked Jim. “It was alright,” said Jade, “but the CGI wasn’t great. At the end, when the stagecoach was at top speed, none of the wheels were moving!”

“Ah,” smiled Jim. “That’s because those old movies were filmed at 16 frames per second.” Jade’s eyes glazed over as her dad launched into more western nerdery. “Those coaches were called ‘four-yarders’ because the circumference of the back wheels was 4 yards.”

“A yard?” asked Jade. “It’s an old measure, a bit shorter than a metre,” said her father. “The 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’t very quick – Usain Bolt could have run faster.”

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’t be a clash.