This puzzle comes from the New York Times. What is the longest arithmetic progression of positive integers you can construct in which none of the numbers include the digit 9. For example, one such progression is 1, 8, 15, 22, which has length 4.
The longest such progression I've been able to devise has length 72. Can anyone do better? --Bob
Dodge the 9s
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Bob78164
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Dodge the 9s
"Question with boldness even the existence of a God; because, if there be one, he must more approve of the homage of reason than that of blindfolded fear." Thomas Jefferson
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Pastor Fireball
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Re: Dodge the 9s
Nope. That's the best I can do. Increase 1 by 125 a total 71 times to hit a maximum of 8876.
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"In times of crisis, the wise build bridges. The foolish build barriers." --Chadwick Boseman (1976-2020)
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Pastor Fireball
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Re: Dodge the 9s
And it appears that you can also get 72 numbers when you increase by 125,125. So the limit of such an arithmetic progression seems to be 72, and it will presumably work for any n-digit progression where n is divisible by 3 and the digits are 125 repeating.
"[Drumpf's] name alone creates division and anger, whose words inspire dissension and hatred, and can't possibly 'Make America Great Again.'" --Kobe Bryant (1978-2020)
"In times of crisis, the wise build bridges. The foolish build barriers." --Chadwick Boseman (1976-2020)
"In times of crisis, the wise build bridges. The foolish build barriers." --Chadwick Boseman (1976-2020)
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Bob78164
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Re: Dodge the 9s
I don't think this latter one works. The 33rd entry is 4,004,001, so the 34th entry is 4,129,126, which has a 9.Pastor Fireball wrote:And it appears that you can also get 72 numbers when you increase by 125,125. So the limit of such an arithmetic progression seems to be 72, and it will presumably work for any n-digit progression where n is divisible by 3 and the digits are 125 repeating.
But increasing by 1,250,125 should work. --Bob
"Question with boldness even the existence of a God; because, if there be one, he must more approve of the homage of reason than that of blindfolded fear." Thomas Jefferson