Make a mathematical expression whose value is equal to 2 that uses all the digits 0, 1, 2, ... 9 exactly once and uses as few other mathematical symbols as possible.
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2$\begingroup$ Which mathematical symbols are allowed? $\endgroup$– bobbleMay 29 at 5:16
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$\begingroup$ @bobble All mathematical symbols are allowed. $\endgroup$– Will Octagon GibsonMay 29 at 5:23
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2 Answers
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As hinted by @Will Octagon Gibson
A solution not utilising any symbols would use only exponentiation. The easiest solution of this form would be $2^{13456789^0}$ (proof that exponentiation does not utilise symbols can be found here)
Alternatively,
A quick brute force solution gives the following examples using only one symbol (I found a total of 48 solutions of this form):
26970/13485
53814/26907
97302/48651 etc.
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$\begingroup$ Nice! Now try doing it with NO additional symbols (just the 10 digits). $\endgroup$ May 29 at 6:09
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2$\begingroup$ Well done. Could also have been any tower of powers staring by 2^1^(...^...) $\endgroup$– ibi0tuxMay 30 at 14:12
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With no additional symbols, but a bit ugly:
$1^{34567890}2$
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1$\begingroup$ In fact there are too many other solutions e.g. $134^{0^56789}2$. $\endgroup$– WhatsUpMay 30 at 14:43