Question

use 4 times 4 to get 100​

Answer 1

We know that,

$\displaystyle\longrightarrow\sf{100=4\times 25}$

So we may represent 25 in three 4's.

We see that,

$\displaystyle\longrightarrow\sf{25=24+1}$

And,

• $\displaystyle\sf{24=4!}$

• $\displaystyle\sf{1=\dfrac {4}{4}}$

Then,

$\displaystyle\longrightarrow\sf{25=4!+\dfrac{4}{4}}$

Hence,

$\displaystyle\longrightarrow\sf{\underline {\underline {100=4\left (4!+\dfrac {4}{4}\right)}}\quad\quad\dots(1)}$

This is one such possibility I've got. Well, there may be more than one possibility too. Some more possibilities found are,

$\displaystyle\longrightarrow\sf{\underline {\underline {100=\left (4\sqrt4+\sqrt4\right)^{\sqrt4}}}}$

$\displaystyle\longrightarrow\sf{\underline {\underline {100=4!\times 4+\sqrt 4+\sqrt4}}}$

$\displaystyle\longrightarrow\sf{\underline {\underline {100=4!\times 4+\sqrt 4\times\sqrt4}}}$

From (1) we can obtain another ones!

$\displaystyle\longrightarrow\sf{\underline {\underline {100=4\left (4!+\dfrac {\sqrt4}{\sqrt4}\right)}}}$

$\displaystyle\longrightarrow\sf{\underline {\underline {100=4\left (4!+\dfrac {4!}{4!}\right)}}}$

And there should be many more or not!