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Can you guess what comes in place of the question mark?

Table

Here's a text-based version of the table:

+----+----+----+----+
|1536| 48 | 96 | 3  |
+----+----+----+----+
|384 |192 | 24 | 12 |
+----+----+----+----+
|768 | 96 | 48 | 6  |
+----+----+----+----+
|192 | ?  | 12 | 24 |
+----+----+----+----+
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It's:

$384$. Starting from the top-left, go down and do a U'y at the bottom, go up, do a U'y at the top, you get: $1536, 384, 768, 192, ?, 96, 192, 48, 96, \dots$, which is divide by $4$, multiply by $2$, and repeat.

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  • $\begingroup$ You got it. It's correct $\endgroup$ – Ak19 May 4 at 11:55
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It is

$384$. In every row, the product of first two numbers is $73728$ and the product of last two numbers are $288$.

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  • 1
    $\begingroup$ The answer is correct. But there is a much simpler way to find the pattern. $\endgroup$ – Ak19 May 4 at 6:00
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Answer:

384

Explanation:

alternating rows of the same column are halved or doubled

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To simplify the pattern finding, this answer:

Think of how the horse moves in chess. Let's call the final position the horse can go be P. So the bottommost 24 has 24 on its P on the left hand side. The bottommost 12 has 12 on its P on the RHS. The 192 has 192 on its P on RHS so the ? has 192 on its P on LHS. It moves up too. 48 and 96 have 48 and 96 respectively at their Ps on their LHS and RHS respectively.

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  • 2
    $\begingroup$ It is even simple to find it. Think moving up and down. $\endgroup$ – Ak19 May 4 at 7:59

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