Make expressions equal to 1,000 using six 2s

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lookagain

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Use six 2s in each expression, but no other digits/numbers, and these other constraints
below, to make expressions that are equal to 1,000.

This puzzle is in base 10.

You may use:
---------------

subtraction symbol
division symbols
parentheses (for grouping and multiplication)
decimal points
concatenation of digits


You may not use:
-------------------

addition symbol
multiplication symbol
repeating decimals
percent symbols
exponentiation
logarithms
trig functions
floor function
ceiling function
any other functions
any other characters


Try to add to a list of what would become at least a total of eight solutions.
Please hide your solutions.

Some examples of concatenation of digits, without or with decimal points, are:
22, .2, 2.2, 22.2, and .22.
 
Last edited by a moderator:
lookagain said:
Use six 2s in each expression, but no other digits/numbers, and these other constraints
below, to make expressions that are equal to 1,000.

This puzzle is in base 10.

You may use:
---------------

subtraction symbol
division symbols
parentheses (for grouping and multiplication)
decimal points
concatenation of digits


You may not use:
-------------------

multiplication symbol
repeating decimals
percent symbols
exponentiation
logarithms
trig functions
floor function
ceiling function
any other functions
any other characters


Try to add to a list of what would become at least a total of eight solutions.
Please hide your solutions.

Some examples of concatenation of digits, without or with decimal points, are:
22, .2, 2.2, 22.2, and .22.
Click to expand...
What about addition?
 
Three solutions are listed so far in the thread. For a couple of hints to two more of the eight (or so)
solutions, consider these:

Make a denominator equal to .02 by
using three of the 2s, parentheses, and decimal points as (.22 - .2) in the expression.


Make a denominator equal to .002 by
using five of the 2s, parentheses, and decimal points as (.222 - .22) in the expression.
 
lookagain said:
Make a denominator equal to .02 by
using three of the 2s, parentheses, and decimal points as (.22 - .2) in the expression.
Click to expand...
(22 - 2) / (.22 - .2)

Make a denominator equal to .002 by
using five of the 2s, parentheses, and decimal points as (.222 - .22) in the expression.
Click to expand...
2 / (.222 - .22)

[imath]\;[/imath]
 
Here are hints for others (I have not given the role of all six 2s in the descriptions necessarily):

Write the denominator using certain 2s and decimal points as an expression equal to .008, and write
the numerator as an expression equal to 8 in two different ways for two different solutions.

Use a denominator of .22 as part of the expression, and either multiply by (2/.2), or divide by (.2/2).

Use (2/.2) twice as factors as part of the expression.

2(2/.2) is another way of expressing 20. Look at the fourth solution given in the thread for making
an alternative.

(.2)(.2) = .04 for a denominator, and (22 - 2) can make 20 for part of a numerator.
 
Please check your answers. I won't be posting more in the thread, unless someone wants more input.

Write the denominator using certain 2s and decimal points as an expression equal to .008, and write
the numerator as an expression equal to 8 in two different ways for two different solutions.
\(\displaystyle \dfrac{(2)(2)(2)}{(.2)(.2)(.2)}\)


Use a denominator of .22 as part of the expression, and either multiply by (2/.2), or divide by (.2/2).
(2/.2)(22/.22)


Use (2/.2) twice as factors as part of the expression.
(2/.2)(2/.2)/(.2/2)


2(2/.2) is another way of expressing 20. Look at the fourth solution given in the thread for making
an alternative.
2(2/.2)/(.22 - .2)


(.2)(.2) = .04 for a denominator, and (22 - 2) can make 20 for part of a numerator.
\(\displaystyle \dfrac{2(22 - 2)}{(.2)(.2)} \)
 
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