# Another Logic Problem

If  \begin{align}2*6&=7,\\4*2&=72\quad\text{and}\\7*3&=144\end{align}

then,

$$\;\;5*8=\;?\qquad\qquad$$

• Is it relevant that 144 vf n ahzore va gur Svobanppv frdhrapr. – jsm May 3 '18 at 15:35
• the others aren't so why would it matter if 144 is? Just curious about your thinking... – Dr t May 3 '18 at 16:09
• what exactly...did @Mike Earnest just edit here that lends clarity and meaning to the initial post? I didn't see any change. Please explain. – Dr t May 3 '18 at 16:33
• @Drt I removed the [logical-deduction] tag and replaced it with [pattern], since this puzzle cannot be solved by logical inference alone. – Mike Earnest May 3 '18 at 16:37
• Your multiplication is wrong. – Rajan May 5 '18 at 11:58

Not sure about any mathematic operation but can find this pattern(could be wrong!):

$2∗6 = 7$;
$4∗2 = 72$; 7 from RHS of 1st row and 2 1st number in 1st row.
$7∗3 = 144$; 7*2 from RHS of 2nd row(multiply) and 4 1st number in 2nd row.

So,

$5∗8 = 167$; $1*4*4$ from RHS of 3rd row and 7 1st number in 3rd row.

edit: just noticed i mistaken 7 with 17, so corrected;)

I found the same pattern as @Preet, but had a different result:

$2 * 6 = 7 \Rightarrow 7$; initial statement
$4 * 2 = 72 \Rightarrow 7$ ~ $2$; product of previous result (just 7) & first row (2)
$7 * 3 = 144 \Rightarrow 14$ ~ $4$; product of previous result $(7*2 = 14)$ and first row (4)
$5 * 8 = 567 \Rightarrow 56$ ~ $7$; product of previous result $(14*4 = 56)$ and first row (7)

$567.$

Strip out the symbols and multiply by 16 to find the next row

2*6=7 => 267 * 16 = 4272
4*2=72 => 4272 * 16 = 73144
7*3=144 => 73144 * 16 = 581704
therefore: 5*8=1704

• $4272\cdot16=68352$ and $73144\cdot16=1170304$? Or just note that the products of the units digits don't even match? Or that $581703$ is odd? – noedne May 4 '18 at 19:35
• edited to correct – omikes May 4 '18 at 19:52
• How are you obtaining these numbers? – noedne May 4 '18 at 19:56
• Yes, I agree with @noedne, the second and third products aren't correct. – hexomino May 4 '18 at 20:06