Write, with four fours and mathematical signs, an expression that is equal to a given integer. The expression cannot include (in addition to the four fours) any number, or letter, or algebraic symbol involving a letter, such as: log., Lim., Etc. ”
Calculating patients affirm that it is possible to write, with four fours, all the whole numbers, from 0 to 100. In certain cases, it will be necessary to use the factorial sign (!) And the square root sign. The cube root cannot be used, because of index 3.
Form the numbers: 25, 24, 97
Attempt:
$100$ is $25\times4$, which seems like a promising number. We know that $4!=24$, and $24\times4=96$. Adding $4$ gives us $100$
So, $25=\dfrac{4\cdot 4! + 4}{4}$
Correct?
If you have to use exactly four times the number $4$, here you can have $24$ and $97$ : $$24 = 4\sqrt{4} + 4*4$$ and $$97 = (4!)*4 + (4/4)$$