Cubed. - Not so logical... again.

Level 2

What number should be in the square such that the sequence has a particular pattern?

174 , 318 , □ , 767 , 1331 , . . . \large 174, 318, \square, 767, 1331, ...

This is part of the series: " It's easy, believe me! "


The answer is 517.

Thành Đạt Lê by Thành Đạt Lê , 17, Singapore

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1 solution

17 4 ( 9 ) = 14 8 ( 10 ) ∣ 14 8 ( 9 ) = 12 5 ( 10 ) = 5 ( 10 ) 3 31 8 ( 9 ) = 26 0 ( 10 ) ∣ 26 0 ( 9 ) = 21 6 ( 10 ) = 6 ( 10 ) 3 517 ( 9 ) = 42 1 ( 10 ) ∣ 42 1 ( 9 ) = 34 3 ( 10 ) = 7 ( 10 ) 3 76 7 ( 9 ) = 62 8 ( 10 ) ∣ 62 8 ( 9 ) = 51 2 ( 10 ) = 8 ( 10 ) 3 133 1 ( 9 ) = 100 0 ( 10 ) ∣ 100 0 ( 9 ) = 72 9 ( 10 ) = 9 ( 10 ) 3 \large 174_{(9)} = 148_{(10)} | 148_{(9)} = 125_{(10)} = 5^3_{(10)} \\ \large 318_{(9)} = 260_{(10)} | 260_{(9)} = 216_{(10)} = 6^3_{(10)} \\ \large \boxed{517}_{(9)} = 421_{(10)} | 421_{(9)} = 343_{(10)} = 7^3_{(10)} \\ \large 767_{(9)} = 628_{(10)} | 628_{(9)} = 512_{(10)} = 8^3_{(10)} \\ \large 1331_{(9)} = 1000_{(10)} | 1000_{(9)} = 729_{(10)} = 9^3_{(10)} \\

1 Helpful 0 Interesting 0 Brilliant 0 Confused

Interesting that 1331 is also a cube in base 10.

Henry U - 2 years, 6 months ago

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That's correct. 1331 = 1 1 3 1331 = 11^3 . It gives out a subtle clue to the problem solvers.

Thành Đạt Lê - 2 years, 6 months ago

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