Total Is Twelve

Can you circle exactly four of these numbers such that the total is twelve?

1 6 1
6 1 6
1 6 1
6 1 6




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Using the clues below, what four numbers am I thinking of?

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There are no duplicate numbers.

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Amazing Facts

No Solution

In 2007, a puzzle was released and $2 million prizes were offered for the first complete solution. The competition ended at noon on 31 December 2010, with no solution being found. Wiki