# Compact mathematical expression [closed]

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.

• Which mathematical symbols are allowed? May 29 at 5:16
• @bobble All mathematical symbols are allowed. May 29 at 5:23

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.

• Nice! Now try doing it with NO additional symbols (just the 10 digits). May 29 at 6:09
• Well done. Could also have been any tower of powers staring by 2^1^(...^...) May 30 at 14:12

With no additional symbols, but a bit ugly:

$$1^{34567890}2$$

• In fact there are too many other solutions e.g. $134^{0^56789}2$. May 30 at 14:43