![(2:2)\cdot(2:2)=1\\2:2 + 2:2=2\\2\cdot2-2:2 =3\\2\cdot2- 2+2=4\\2 :2 +2 +2 =5\\2\cdot2\cdot2 -2 =6\\\\-\log_2\log_2\sqrt{\sqrt{\sqrt{\sqrt{\sqrt{2}}}}}+2=7\\\\2 + 2 + 2 + 2=8\\(2+2:2)^2=9\\\\\underline{\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad}\\\\-\log_2\log_2\sqrt{\sqrt{\sqrt{\sqrt{\sqrt{2}}}}}+2=-\log_2\log_22^{\frac{1}{32}}+2=-\log_2\frac{1}{32}+2=\\\\=-\log_22^{-5}+2=-(-5)+2=5+2=7](https://tex.z-dn.net/?f=%282%3A2%29%5Ccdot%282%3A2%29%3D1%5C%5C2%3A2+%2B+2%3A2%3D2%5C%5C2%5Ccdot2-2%3A2+%3D3%5C%5C2%5Ccdot2-+2%2B2%3D4%5C%5C2+%3A2+%2B2+%2B2+%3D5%5C%5C2%5Ccdot2%5Ccdot2+-2+%3D6%5C%5C%5C%5C-%5Clog_2%5Clog_2%5Csqrt%7B%5Csqrt%7B%5Csqrt%7B%5Csqrt%7B%5Csqrt%7B2%7D%7D%7D%7D%7D%2B2%3D7%5C%5C%5C%5C2+%2B+2+%2B+2+%2B+2%3D8%5C%5C%282%2B2%3A2%29%5E2%3D9%5C%5C%5C%5C%5Cunderline%7B%5Cquad%5Cquad%5Cquad%5Cquad%5Cquad%5Cquad%5Cquad%5Cquad%5Cquad%5Cquad%5Cquad%5Cquad%5Cquad%5Cquad%5Cquad%5Cquad%5Cquad%5Cquad%5Cquad%5Cquad%5Cquad%5Cquad%5Cquad%5Cquad%5Cquad%5Cquad%5Cquad%5Cquad%5Cquad%7D%5C%5C%5C%5C-%5Clog_2%5Clog_2%5Csqrt%7B%5Csqrt%7B%5Csqrt%7B%5Csqrt%7B%5Csqrt%7B2%7D%7D%7D%7D%7D%2B2%3D-%5Clog_2%5Clog_22%5E%7B%5Cfrac%7B1%7D%7B32%7D%7D%2B2%3D-%5Clog_2%5Cfrac%7B1%7D%7B32%7D%2B2%3D%5C%5C%5C%5C%3D-%5Clog_22%5E%7B-5%7D%2B2%3D-%28-5%29%2B2%3D5%2B2%3D7)
Для получения цифры 7 возможны и другие варианты с применением других математических операций.
[a] - целая часть числа a.
![1)\quad[\sqrt{2}]+2+2+2=1+6=7](https://tex.z-dn.net/?f=1%29%5Cquad%5B%5Csqrt%7B2%7D%5D%2B2%2B2%2B2%3D1%2B6%3D7)
lb - это логарифм с основанием 2.
![2)\quad\text{lb} 2 + 2 + 2 + 2 = 1 + 6=7](https://tex.z-dn.net/?f=2%29%5Cquad%5Ctext%7Blb%7D+2+%2B+2+%2B+2+%2B+2+%3D+1+%2B+6%3D7)
С помощью тригонометрической функции:
![3)\quad\displaystyle 2 + 2 + 2 + \sin\bigg(\frac{\pi}{2}\bigg)=6+1=7](https://tex.z-dn.net/?f=3%29%5Cquad%5Cdisplaystyle+2+%2B+2+%2B+2+%2B+%5Csin%5Cbigg%28%5Cfrac%7B%5Cpi%7D%7B2%7D%5Cbigg%29%3D6%2B1%3D7)
n!! - это двойной факториал.
Если n - четное, то это произведение всех четных чисел от 1 до n (2*4*6...*n)
Если n - нечетное, то произведение всех нечетных чисел от 1 до n (1*3*5...*n)
![4)\quad(2+2)!! - 2 : 2 = 4!! - 1 = 2\cdot4-1=8-1=7](https://tex.z-dn.net/?f=4%29%5Cquad%282%2B2%29%21%21+-+2+%3A+2+%3D+4%21%21+-+1+%3D+2%5Ccdot4-1%3D8-1%3D7)