License Nonsense
(pg 77 – 78 in Challenging Whodunit Puzzles by Jim Sukach)
Flora and Fauna were a little frustrated at how easily their cousin Junior figured out which of them has eaten the early breakfast (an earlier mystery, don’t worry your heads about it). At the same time they admired his cleverness. Maybe he was more closely related to them than they thought.
The twins sat in the back seat of Grandpa Quicksolve’s car on their way to Kris Crossing, and Junior sat in the front next to Grandpa. The sisters whispered to each other and decided to give Junior another test.
“I like to look at license plates,“ Flora said.
“There’s one that says MY TOY,“ said Fauna, pointing to a bright red sportscar racing past them.
“Look at the van in front of us,” Grandpa said. The van’s license plate said MOMS BUS.
“I like those special ones,” Flora said, “with words”.
“It seems funny to me when you see one with a name and then a number, like BOB-3. It makes me wonder what happened to BOB-1 and BOB-2”, said Grandpa.
“Maybe it’s a woman who married a lot of men named Bob,” joked Junior.
“Regular license plates have letters and numbers. I wonder why they use letters,” Flora said.
“Maybe they are easier to remember,“ Fauna replied.
“I guess if they use both, they can make more plates,” Junior said.
“Do you suppose they could make more plates if they just used numbers than if they just used letters?” Flora asked, directing her question to Junior.
“That’s an easy question,” Junior answered.
But is the answer easy?
(pg 77 – 78 in Challenging Whodunit Puzzles by Jim Sukach)
Flora and Fauna were a little frustrated at how easily their cousin Junior figured out which of them has eaten the early breakfast (an earlier mystery, don’t worry your heads about it). At the same time they admired his cleverness. Maybe he was more closely related to them than they thought.
The twins sat in the back seat of Grandpa Quicksolve’s car on their way to Kris Crossing, and Junior sat in the front next to Grandpa. The sisters whispered to each other and decided to give Junior another test.
“I like to look at license plates,“ Flora said.
“There’s one that says MY TOY,“ said Fauna, pointing to a bright red sportscar racing past them.
“Look at the van in front of us,” Grandpa said. The van’s license plate said MOMS BUS.
“I like those special ones,” Flora said, “with words”.
“It seems funny to me when you see one with a name and then a number, like BOB-3. It makes me wonder what happened to BOB-1 and BOB-2”, said Grandpa.
“Maybe it’s a woman who married a lot of men named Bob,” joked Junior.
“Regular license plates have letters and numbers. I wonder why they use letters,” Flora said.
“Maybe they are easier to remember,“ Fauna replied.
“I guess if they use both, they can make more plates,” Junior said.
“Do you suppose they could make more plates if they just used numbers than if they just used letters?” Flora asked, directing her question to Junior.
“That’s an easy question,” Junior answered.
But is the answer easy?
1 comment:
I'm not quite sure I got this one right (since they claim is that it is non-obvious), but here goes:
depends on the number of positions (doesn't it always?) and other factors
Numbers can be smaller in space, so one can fit more on a plate. Are we assuming numbers to be 0..9? Or maybe base 16?
Well, I will assume 0..9 and A..Z, which is effectively base 10 and base 26. The base to the power of the number of positions is the range of each (b^p, b to the p power). So, with one position, we could get 10 plates with number vs 26 with letters. Two positions (now we're starting to talk) we get 10x10 vs 26x26. Etc. So, with the assumptions I've made, one can do more with letters (even excluding the bad words... do we need more bad numbers than 69 to keep it fair?) than numbers.
Though, I can not help but think I missed something...
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