# 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?

• I also added the tag (recreational-mathematics). Sorry about not noticing this tag until today. – Jyrki Lahtonen Jul 5 '11 at 7:54
• $438^3 = 84027672$? Or isn't that allowed? – yatima2975 Jul 5 '11 at 10:41
• @yatima2975: That's a clever idea, but to make the "3" a superscript, you have to move all five matches in "3"; can't do it by moving just two. – ShreevatsaR Jul 5 '11 at 15:04
• @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
• @yatima: IIRC you held the record for 4 hours, before Silas posted so please post your suggestion as well, so that we can upvote it! – Jyrki Lahtonen Jul 6 '11 at 16:35

## 4 Answers

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

      _   _  _
|_| _| |_| _|
| _| |_| _|

_   _  _
|_| /\  | |_| _|
|     | |_| _|


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:

             _
_   _  _|
|_| _| |_| _|
| _| |_|


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

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

      _   _  _
|_| _| |_| _|
| _| |_| _|
_   _  _
_ |_| |_| _|
| _| |_| _|
|

• 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 '15 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.

      _   _  _
|_| _| |_| _|
| _| |_| _|

_    _   _  _
| | _| |_| _|
| | _|  _| _|

      _   _  _
|_| _| |_| _|
| _| |_| _|

_   _
|_| _| |_| _
| _| |_||_|
|


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

      _   _
|_| _| |_| _
| _| |_| _|
_|


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

• You moved three matches? – Pedro Tamaroff Jul 30 '15 at 2:03
• @PedroTamaroff -- Oops, thanks -- corrected now with only two matches moved. – r.e.s. Jul 30 '15 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 '15 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 '15 at 3:17

## protected by SurbDec 11 '15 at 22:33

Thank you for your interest in this question. Because it has attracted low-quality or spam answers that had to be removed, posting an answer now requires 10 reputation on this site (the association bonus does not count).

Would you like to answer one of these unanswered questions instead?