When I searched through my dictionary, the following words were the best (or tied for the best) for a certain property. What is that property?
a
ay
may
ahoy
flays
maizes
blowzier
capsuling
ambidextrously
13
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15
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First try: I think the letters of each of the words are the:
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Second go after first go was zapped by OP. Now think the letters of each of the words are the:
Most spaced out for words of given length. They have the largest least value of the set of A1 - Z26 differences of the letters when written alphabetically. Could say the least closest friendship.
Working out:
a - single letter words have 0 difference.
ay → 1-25 = 24
may → 1-13-25 → min {12, 12} = 12
ahoy → 1-8-15-25 → min {7, 7, 10} = 7
flays → 1-6-12-19-25 → min {5, 6, 7, 6} = 5
maizes → 1-5-9-13-19-26 → min {4, 4, 4, 6, 7} = 4
blowzier → 2-5-9-12-15-18-23-26 → min {3, 4, 3, 3, 3, 5, 3} = 3
capsuling → 1-3-7-9-12-14-16-19-21 → min {2, 4, 2, 3, 2, 2, 3, 2} = 2
ambidextrously → 1-2-4-5-9-12-13-15-18-19-20-21-24-25 → min { 1, 2, 1, 4, 3, 1, 2, 3, 1, 1, 1, 3, 1} → 1
And I think words of greater length than 14 have largest minimum of 0
Note: zap → 1-16-26 → min {15,10} has min 10 so is beaten by may min of 12
lazes → 1-5-12-19-26 → min {4, 7, 7, 7} has min 4 so is beaten by flays min of 5
First try: I think the letters of each of the words are the:
most spaced out for words of each given length. So these words give the greatest product when the A1Z26 differences of the letters of the words, sorted in alphabetical order, are multiplied.
Examples for the words:
a - single letter words have empty product = 1
ay (not counting 'za for pizza) → 1-25 = 24
may = amy → 1-13-25 → 12.12 = 144
ahoy → 1-8-15-25 → 7.7.10 = 490
flays → 1-6-12-19-25 → 5.6.7.6 = 1260
maizes → 1-5-9-13-19-26 → 4.4.4.6.7 = 2688
blowzier → 2-5-9-12-15-18-23-26 → 3.4.3.3.3.5.3 = 4860
capsuling → 1-3-7-9-12-14-16-19-21 → 2.4.2.3.2.2.3.2 = 1152
ambidextrously → 1-2-4-5-9-12-13-15-18-19-20-21-24-25 → 1.2.1.4.3.1.2.3.1.1.1.3.1 → 432
...and if there was a 26 letter word the highest value it could have would be 1.
Therefore blowzier is special as it:
gives the maximum value of these products at 4860.
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$\begingroup$ You're on the right tract, but that's not quite it. For instance,
zapis in my dictionary, butmayis better.lazesis in my dictionary, butflaysis better. $\endgroup$ – isaacg Sep 3 '18 at 16:25 -
$\begingroup$ @isaacg - Nice counterexamples. I've tried again! $\endgroup$ – Tom Sep 3 '18 at 17:27
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