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Puzzling Weekend! UVc is back again with Lots of Magic... Enjoy the Show!

Given: LOTS is being multiplied by F to yield MAGIC.

Digit 0 to 9 are all represented by ten different letters in this multiplication Alphametic.

LOTS, MAGIC represent two concatenated Numbers.

$ LOTS $ X $F$ = $MAGIC$

Clues:

1) F represents 3,

2). M, G, C are consecutive, but may not be in order.

3). A, I are also consecutive.

4). Also, LOTS contain 3 consecutive digits not necessarily in order. One of the consecutive digits adds upto rest of the two consecutive digits.

Figure them out and Enjoy the Show!!!

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  • $\begingroup$ the rest instead of test? $\endgroup$ – Omega Krypton May 18 at 15:11
  • $\begingroup$ Thx for catching it. $\endgroup$ – Uvc May 18 at 15:12
  • $\begingroup$ welcome:) according to (4), the 3 digits must be 1,2,3. yet F=3. possible error? $\endgroup$ – Omega Krypton May 18 at 15:12
  • $\begingroup$ F is the multiplying digit...I wanted to bring it down to show it better..LOTS is being multiplied by single digit F to yield MAGIC. $\endgroup$ – Uvc May 18 at 15:15
  • $\begingroup$ i mean will one of LOTS repeat with F? $\endgroup$ – Omega Krypton May 18 at 15:16
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Partial

$M=$

$1$ or $2$

Since $F=3$

Even if $L = 9$, $M$ would also be $2$. Carry is not possible since $M$ would then be 3 ($M=F$)

$L>$

$3$ (since only then there would be carry)

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5
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It's:

$5694\times3=17082$

Because:

$F=3$. $M=1,2$, and so $MGC=\{0,1,2\}$, but $C\ne0$. As $M+G+C=3$ and our answer is divisible by $3$, $3|(A+I)$, so $A+I=4+5, 7+8$. From clue 4, $A+I=7+8$, and $LOTS=\{4,5,6,9\}$. $S=4$ as $3\times4=2$, and no other value produces an output in the range required, so $C=2, M=1, G=0$. The rest I guessed.

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  • $\begingroup$ Note that last hint that the sum of two consecutive digits in LOTS must add up to the third, but $4+5\ne 6$. $\endgroup$ – TheSimpliFire May 18 at 15:36
  • $\begingroup$ @TheSimpliFire; I think he means $4+5=9$. $\endgroup$ – JMP May 18 at 15:37
  • $\begingroup$ How did you deduce M = 1,2 ? $\endgroup$ – NoLand'sMan May 18 at 15:50
  • $\begingroup$ @NoLand'sMan; LOTS is at most 9876, which would make M=2, or it could be 1. I assumed it was not zero, because leading zeroes are frowned on. $\endgroup$ – JMP May 18 at 15:54
  • $\begingroup$ Note \mid for $\mid$. $\endgroup$ – TheSimpliFire May 18 at 15:56

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