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# How to make digits 1-100 with 2, 0, 2, 2

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This is also known as the 2022 problem.

The instructions for this assignment are:

Use the digits in the year 2022 and the operations +, -, x, ÷, √ (square root), ^ (raise to a power), “!” (factorial), combinations and permutations — along with parentheses, brackets, or other grouping symbols — to write expressions for the counting numbers 1 through 100.

All four digits must be used in each expression.

Only the digits 2, 0, 2, 2 may be used.

The decimal point may be used, as in .2, .02, etc. (repeating decimals as well)

Multi-digit numbers such as 20 or 202 may be used.

Double (!!), triple (!!!) or larger factorials are not permitted

Dec 28, 2021

#1
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https://web2.0calc.com/questions/how-to-make-digits-1-100-with-2-0-2-1

Dec 29, 2021
#2
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1 = (sqrt(2) * sqrt(2)) : 2 + 0

2 = 2 - 2 + 2 - 0

3 = (2^0 + 2)! : 2

4 = sqrt(2^2) - 0 + 2

5 = 2^0 + 2 + 2

6 = 2 + 0 + 2 + 2

7 = 2 + 2 + 2 + 0!

8 = 2 * 2 * 2 - 0

9 = 0! + (2 * 2 * 2)

10 = 22 : 2 - 0!

11 = 22 : 2 + 0

12 = (2 + 2)! : 2 - 0

13 = (2 + 2)! : 2 + 0!

14 = ((2 + 0!)! * 2) + 2

15 = ((2^2)^2) - 0!

16 = ((2^2)^2) + 0

17 = ((2^2)^2) + 0!

18 = 20 - (sqrt(2) * sqrt(2)) + 0

19 = 22 - 2 - 0!

20 = 20 - (2 - 2)

21 = (2 + 2)! - 2 - 0!

22 = 20 + (sqrt(2) * sqrt(2))

23 = 22 + (2 - 0!)

24 = (2 + 2)! + (sqrt(2) * 0)

25 = (2 + 0! + 2)!

26 = (2 + 2)! + 2 - 0

27 = (2 + 2)! + 2 + 0!

28 = 22 + (0! + 2)!

...

Dec 30, 2021
#3
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29 = (2+2)! + 0!/.2

30 = 20 + 2/.2

Jan 1, 2022
edited by Guest  Jan 1, 2022