# Anyone want to try (L+O+G+I+C)^3 =LOGIC

5 different digits, not much logic required, less than 20 possibilities! Logic is not often in evidence here, I have no reserve in telling you!

So, the L, O, etc would be unknowns?
sure, all single digits, and all different, L cannot be zero, and the cubed number must be between 22 and 46 inclusive to be 5 digits. 98765 > 46^3 >= LOGIC >= 22^3 > 10234. In fact from 98765 we know that L+O+G+I+C <= 35 but 35^3 = 43875 so L+O+G+I+C<=34 and thus L<=3 and again therefore L+O+G+I+C<=33
and LOGIC <=33^3=35937.
Can L be 1? Yes provided 22 <= L+O+G+I+C <=27 since 27^3=19683.
Can L be 2? Yes provided 28 <= L+O+G+I+C <=31 since 31^3=29791
Can L be 3? Yes of course, provided 32 <= L+O+G+I+C <=33
We can also see 31 and of course 30 are ruled out by repeated digits.
In fact only 23,25,26,28,30,31,33 have cubes within range having no digit repetition.
No further logic is required or useful! The answer is already in the text of this comment.
Well, assuming that L, O, etc are single digit whole numbers, then L, O, G, I, C elementOf [0, 1, ..., 9]. There is 10C5 = 252 combinations. So, if we had to take a brute force approach, we'd have a few computations to deal with.
1+9+6+8+3=27
27^3=19683

L=1
O=9
G=6
I=8
C=3
Logic is a bird tweeting in a meadow. - Spock, 1966.

As for that other rubbish, you did not explain the approach or method... making it NON logical.
No surprise.
I hit the wrong button.

Is that message for me Bob?
26 works too.
No other numbers work as far as I can see.
Actually 26 doesnâ€™t work, sorry.

So only 27 works.
Well, frankly, if L, O, etc are digits (single), then this equation does not have a solution.
Alright. I get it from Merlot post. This is not an equation and it is not math either. Is a puzzle I suppose. So, LOGIC =/= L*O*G*I*C. That defies math convention which throws me off immediately.

Anyhow, if I understood correctly, then the followings are all solutions:

L=0,O=4,G=9,I=1,C=3
L=0,O=5,G=8,I=3,C=2
L=1,O=9,G=6,I=8,C=3
Of course Merlot is correct and Agentbob as always speaks just nonsense. As I said, the answer was in the comment, where 27^3 was explicitly mentioned. As a follow-up you might try C^L = LOGIC. These come from the mathsisfun.com site.
22,24,27,29,32 should have been the list of possible candidates based on unique digits, whereas I listed the numbers with repeated digits.

Permit me to make special mention of @Agentbob as an agent against logic!
Ans:

L=7, O=8, G=1, I=2, C=5

PS:
Why cannae L be zero? Is there a specific reason or is that just a condition/restriction?
We do not write numbers with leading zeros, except for 0 itself.
or decimals like 0.00001428570000142857...
59049
Agreed. Though mathematically, the following holds:

(0+4+9+1+3)^3 = 4913 = 04913 = 004913 = 0004913 = etc.

Anyhows. Good puzzle/s. Cheers.
Ok, Joe's is the only one, in my excitement I never checked the individualty.
So Logic = LOGIC.

I'm so impressed.
These puzzles are only for boring old bstrds like us three, pal. I find them kinda better than you typical pub quizz though. We ole geezers should meet up somewhere, someday and have a nerding session over a few pints of guinness and handfuls of peanuts.
Robert, pal, init time you stop bugging this fargo chap here, aye? Lets all try to get along, shalt we?
@ Joe. F Y I.... think again.

Before you got here , the Fargo entity drew 1st blood by making repeated non sensical comments on my blogs... always making reference to "4 cheeses"..
.as though that syntax represented some kind of Trump card in the CStepford Experience we've all come to love...
Furthermore, you notice he has this habit of putting others down-- even in the opening of this current non logical gibbering concerning logic = Logic...such a stunning piece of logic. Like eYe said, very impressed.
I don't normally do puzzles or maths, that's not my background so I just chance my arm. Anyway, Fargo gave us the answer.
Fargo did but he didn't give us all the answers. By the definition of the equality sign, I still sustain that the two other solutions I proposed, which require L to be 0, are valid.
The only place I've seen leading 0's in practical use is on mileometers / speedometers. However, regardless of 0's in use in complicated maths, the rules given in this game stated that L could not be 0, so that's good enough for me.
p.s. I hate maths.
Another example of these alphabet puzzles is SEND + MORE = MONEY where there are 8 different digits. Obviously M=1 and O=0 (since S+M+carry=S+1+carry <>1!)
Keep going from there. S is 8 or 9.
I guess the solution you are after is:
S=9 E=5 N=6 D=7 M=1 O=0 R=8 Y=2
9567+1085=10652

But really, in addition to the one above, the following are all solutions:
S=6 E=4 N=1 D=9 M=0 O=7 R=2 Y=3
6419+724=7143
S=3 E=7 N=1 D=2 M=0 O=4 R=6 Y=9
3712+467=4179
S=8 E=4 N=3 D=2 M=0 O=9 R=1 Y=6
8432+914=9346
S=3 E=8 N=2 D=1 M=0 O=4 R=6 Y=9
3821+468=4289
S=8 E=3 N=2 D=4 M=0 O=9 R=1 Y=7
8324+913=9237
S=7 E=4 N=2 D=9 M=0 O=8 R=1 Y=3
7429+814=8243
S=7 E=5 N=3 D=1 M=0 O=8 R=2 Y=6
7531+825=8356
S=6 E=8 N=5 D=3 M=0 O=7 R=2 Y=1
6853+728=7581
S=2 E=8 N=1 D=7 M=0 O=3 R=6 Y=5
2817+368=3185
S=7 E=3 N=1 D=6 M=0 O=8 R=2 Y=9
7316+823=8139
S=2 E=8 N=1 D=9 M=0 O=3 R=6 Y=7
2819+368=3187
S=8 E=5 N=4 D=2 M=0 O=9 R=1 Y=7
8542+915=9457
S=5 E=7 N=3 D=1 M=0 O=6 R=4 Y=8
5731+647=6378
S=6 E=4 N=1 D=5 M=0 O=7 R=3 Y=9
6415+734=7149
S=3 E=7 N=1 D=9 M=0 O=4 R=5 Y=6
3719+457=4176
S=7 E=5 N=3 D=9 M=0 O=8 R=1 Y=4
7539+815=8354
S=6 E=8 N=5 D=1 M=0 O=7 R=3 Y=9
6851+738=7589
S=7 E=6 N=4 D=9 M=0 O=8 R=1 Y=5
7649+816=8465
S=6 E=5 N=2 D=4 M=0 O=7 R=3 Y=9
6524+735=7259
S=5 E=7 N=3 D=2 M=0 O=6 R=4 Y=9
5732+647=6379
S=7 E=5 N=3 D=4 M=0 O=8 R=2 Y=9
7534+825=8359
S=3 E=8 N=2 D=9 M=0 O=4 R=5 Y=7
3829+458=4287
S=7 E=6 N=4 D=3 M=0 O=8 R=2 Y=9
7643+826=8469
S=5 E=8 N=4 D=9 M=0 O=6 R=3 Y=7
5849+638=6487
M is not zero - conventionally we DO NOT WRITE NUMBERS WITH A LEADING ZERO! m=1
@joseph using Excel perchance? The idea is to use logic and deduction if possible ... m by convention, s, cannot be zero

2. Your convention is only your own. No such thing exists in mathematics. Leading zeros are implied. That is why you can leave them out and we often do (less writing is better) but you are absolutely free to include them and would be absolutely correct in doing so.

3. Good fkn night
@jos twit - how many twit's are prime, and how many have 3 prime factors. Review your words and mine. Idiots take offence at uppercase when uppercase is merely intended as emphasis. Again I say ... twit.
Convention is convention. A leading zero except for 0 itself and 0.x is redundant. We do not use it. This is not just a convention but a rule.
Educate yourself about online etiquette. This is not fn 1903, yae ole fud!

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## FargoFan

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Retired but teaching and studying every day, travelling whenever I can and at home wherever I happen to be. From a small family but wishing I were part of a larger one. My students are scattered all over the world, as is my family. Language is a part [read more]