Using the digit 2 four times, with no other symbols, make the largest number possible.

An example is 222², but a higher result is possible by repositioning the 2's.

Following is a list of numbers, from smallest to largest, using four 2s with no additional symbolic notation - (only subscription and superscription).

Bullet points 1 and 2 show numbers with a radix - the subscripted numbers to the right of the base number.The absence of the radix is the default for numbers represented in base 10.

Bullet points 3-9 and 11 show numbers with exponentiation - superscripted number(s) to the right. This notation
is also called the exponent or power of the base number.

Bullet points 10 and 12-17 show numbers with tetration - superscripted number(s) to the left of of the base
number. Tetration is also known as iterated exponentiation, super-exponentiation, and hyperpower.

1. 2₂₂₂ = (2 * 222⁰) = 2
2. 22₂₂ = (2 * 22¹) + (2 * 22⁰) = 46
3. 2222 = 2222
4. 222² = 49284
5. 2²²² = 2¹⁶ = 65536
6. 22²² = 22⁴ = 234256
7. 22²² ~= 3.41428 * 10²⁹
8. 2²²² ~= 6.73999 * 10⁶⁶
9. 2²²² = 2⁴⁸⁴ ~= 4.9948 * 10¹⁴⁵
10. ²222 = 222²²² ~= 7.77689 * 10⁵²⁰
11. 2²²² = 2^4194304
12. ²²22 = 22²²²²²² [22 is chained 4 times]
13. ²²22 = 22^22..22 [22 is chained 22 times]
14. ²²²2 = 2^2..2 [2 is chained 222 times]
15. ²²²2 = 2^2..2 [2 is chained 2¹⁶ times]
16. ²²²2 = 2^2..2 [2 is chained 22²² times]
17. ²²²2 = 2^2..2 [2 is chained N times where
    N = 2^2..2such that 2 is chained 22 times]

Posted by Dej Mar on 2007-11-20 11:49:23