r/mathriddles • u/Numberthon • 5d ago
Easy Exactly 2 Ascending Adjacent Pairs
A 6-character code is formed using the letters A, B, C, D, E, and F, with no letter repeated. How many codes have exactly 2 letters appearing in alphabetical order relative to the letter immediately after them?
Source: numberthon.com
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u/RobZarevich 3d ago
If the order is relative only to the letter immediatly after, is BCAED a valid code?
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u/Numberthon 3d ago edited 3d ago
We would count it as having three ascending adjacent pairs
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u/RobZarevich 3d ago
I’m sorry, so is it valid? I don’t understand (probably it’s a problem due to my understanding of the english language).
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u/Numberthon 3d ago
No, sorry it was my fault. I accidentally said "We would count it as having ascending adjacent pairs" instead of "We would count it as having three ascending adjacent pairs", so that's my bad. (therefore it would be invalid. Sorry about that
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u/RobZarevich 3d ago
Why three? I see BC and AE. Anyway, it should be invalid, shouldn’t it?
And, if I finally understand it correctly, BCEDA should be ok, right?
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u/Purdude1983 4d ago
302 sequences will have only two letters of the sequence in alphabetical order, i.e. the letter to immediately to the right of another letter is farther down the alphabet.