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Home » So, number of 8-digit numbers **without** consecutive 3s is 55. - Get link 4share

So, number of 8-digit numbers without consecutive 3s is 55. - Get link 4share

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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Solution: Let the four consecutive integers be $ n, n+1, n+2, n+3 $.
Among any four consecutive integers:
There are at least two even numbers, and one of them is divisible by 4...
There is exactly one multiple of 4 and another even, so $ 8 \mid $ pro...
There is at least one multiple of 3 → $ 3 \mid $ product
There is no guaranteed factor of 5 or higher
So the product is always divisible by $ 8 \cdot 3 = 24 $. But can we d...
Check more precisely:
The product includes:
At least one multiple of 3 → $ 3 $

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