# What is the highest number that can be got from 4383 by moving exactly 2 matches?

What is the highest number that can be got from 4383 by moving exactly 2 matches?

Number 1 has got 2 matches, so I thought it will be 47831 as I remove two matches from second number (3), but it isn't the highest possible.

Format is same like this (1 is only number with only two matches)

Does anybody know solution?

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Please do not use [homework] as a sole tag. Surely you know from which class you took the exercise, so please add the topic as a tag of the question. – Asaf Karagila Jul 4 '11 at 11:51
edited .... can you help now? – genesis Jul 4 '11 at 11:53
I felt that (puzzle) is the most appropriate tag, so I added it. If this really is homework, then you are having fun at school! – Jyrki Lahtonen Jul 4 '11 at 12:02
$438^3 = 84027672$? Or isn't that allowed? – yatima2975 Jul 5 '11 at 10:41
@ShreevatsaR: you can put the lower two matches on top, as the 'normal' and the superscripted 3 overlap. – yatima2975 Jul 5 '11 at 15:15

If you want to play with notation, you could have 4^783 or $438^3$ depending on what you allow.

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Of course with actual matches, the caret would be squished in between the 4 and the 3. Might be considered cheating because really you should move the whole 4, as I did in the drawing. On the other hand:

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Only moves 2 matches and would be how you would write $438^3 = 84,027,672$

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7^983 is the highest number. The 4 changes to a 7, and the 3 changes to a 9.

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That's even better :) – yatima2975 Jul 5 '11 at 15:04
+1 It took me a while to see how you did it, but I got it in the end. Well done! – Jyrki Lahtonen Jul 5 '11 at 19:16
$^{438}3$ (tetration notation) is enormously larger than any other answer so far. – r.e.s. Jul 30 at 3:20

I am guessing 71393. Rotate the horizontal match of the leading 4 to split it into two ones, and grab one out of the 8 to turn the leading 1 into a 7.

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or (if that's not a valid $9$),

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$^{438}3= 3^{3^{\cdot^{\cdot^{3^3}}}}$ (an exponential tower with $438\ \ 3$s).

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You moved three matches? – Pedro Tamaroff Jul 30 at 2:03
@PedroTamaroff -- Oops, thanks -- corrected now with only two matches moved. – r.e.s. Jul 30 at 2:05
An LED-style 9 is supposed to have the bottom horizontal bar. What you have there looks more like a q. – Rahul Jul 30 at 2:43
@Rahul -- Thanks -- It can be a $3$ if the $9$ isn't valid. (Either one is enormously larger than any of the other answers.) – r.e.s. Jul 30 at 3:17