# Uvc with Lots of Magic… Enjoy the Show!

## 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!!!

• the rest instead of test? – Omega Krypton May 18 at 15:11
• Thx for catching it. – Uvc May 18 at 15:12
• welcome:) according to (4), the 3 digits must be 1,2,3. yet F=3. possible error? – Omega Krypton May 18 at 15:12
• 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. – Uvc May 18 at 15:15
• i mean will one of LOTS repeat with F? – Omega Krypton May 18 at 15:16

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)

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.

• Note that last hint that the sum of two consecutive digits in LOTS must add up to the third, but $4+5\ne 6$. – TheSimpliFire May 18 at 15:36
• @TheSimpliFire; I think he means $4+5=9$. – JMP May 18 at 15:37
• How did you deduce M = 1,2 ? – NoLand'sMan May 18 at 15:50
• @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. – JMP May 18 at 15:54
• Note \mid for $\mid$. – TheSimpliFire May 18 at 15:56