my recreational arithmetic challenge

lookagain

Elite Member
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Aug 22, 2010
Messages
3,230
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For my 1,000th post, I want you to form at least one expression

that equals 1,000. These expressions are meant to be typed on at

least the Ti-83 Plus or lower-numbered graphics calculators.

They will work there.


Rules:
------

The expressions will use the Order of Operations (the PEMDAS system).

Use exactly four 1s and no other digits.

Use no more than three "/" symbols for division.

Use no more than three "*" symbols for multiplication.

Use no more than three "." symbols for decimal points.

Use no more than two pairs of parentheses.

Concatenation is not permitted. For instance, as part of the expressions,
these are not allowed:

11
111
1111
1.1
1.11
1.111
11.1
11.11
111.1
.11
.111
.1111

-----------------------

No square roots, no other roots, no factorial symbols, no addition signs,
no subtraction signs, no negative signs, and no exponentiation are allowed.

If an expression can have one or more sets of parentheses removed,
and the resultant expression still equals 1000, then count the
expression with fewer characters to be the solution (or one of the
solutions as the case may be).

For the sake of an example where the target value is .01 and exactly
three 1s are to be used, you would use

".1*.1/1" instead of "(.1*.1)/1" for the/a solution.
 
1/(.1*.1*.1)?
. . . . . Yes.


Denis said:
Four 1's and nothing else: . . . . . Yes, I missed this solution.
|\/|


Can anyone find any more solutions that are in the style of daon2's solution?


Edit
-----


Here is another one:

1/.1/.1/.1



Can any more be found?
 
Last edited:
a la serious: 1 / .1 / (.1 * .1) . . . . . . Yes.


Edit: There is at least another solution in the style of Denis's in this quote box
and of daon2's solution that has not been posted yet.
 
Last edited:
Edit: There is at least another solution in the style of Denis's in this quote box
and of daon2's solution that has not been posted yet.

The final solution that I found (but not necessarily the last solution) is the following:

1/(.1 * .1)/.1
 
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