# 4x4 number grid with one empty cell

Can you guess what comes in place of the question mark? Here's a text-based version of the table:

1536 48 96 3
384 192 24 12
768 96 48 6
192 ? 12 24

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.

• You got it. It's correct
– Ak.
May 4 '19 at 11:55

It is

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

• The answer is correct. But there is a much simpler way to find the pattern.
– Ak.
May 4 '19 at 6:00

384

Explanation:

alternating rows of the same column are halved or doubled

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.

• It is even simple to find it. Think moving up and down.
– Ak.
May 4 '19 at 7:59