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694 and Level 6

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Level 6 puzzles aren’t easy, but do give it a try! There are hints at the bottom of the page.

Print the puzzles or type the solution on this excel file: 10 Factors 2015-11-23

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Here are some ways that 694 is a special number:

694 is the 22nd centered triangular number because it is the sum of these consecutive triangular numbers 210, 231, 253.

Notice that 21(22)/2 is 231, the number in the middle of those consecutive triangular numbers. Also notice that 3(231) + 1 = 694.

694 BASE 10 becomes palindrome 1C1 in BASE 21 because C Base 21 is equivalent to 12 Base 10, and 1(21²) + 12(21) + 1(1) = 694.

 

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