# Make expressions equal to 1,000 using exactly six 1s

• You may use up to two subtraction symbols (no negation symbols).
• You may use up to two decimal points.
• You will use one vinculum for division (no "/").
• You may use concatenation of digits only, including forming numbers which have decimal points in them.
• You may not use grouping symbols such as parentheses, brackets, or braces.
• You may not use factorial signs.
• You may not use square roots.
• You may not use exponentiation.
• You may not use logarithms.
• You may not use trigonometric functions.
• You may not use any other characters or operations.
• This is in base 10. (The numbers using the ones, and 1,000 on the other side of the equals sign, are in base 10.)

Try to create six different solutions.

• To clarify are you allowed to use any 0's or exclusively the six 1's and decimals? Jan 30 at 17:42
• @gabbo1092 -- No zeroes may be used. You can write .1, 1.1, .11, 1.11, etc., if they would make expressions have the correct value(s). Jan 30 at 18:37
• bin-->dec(1111101000) Jan 31 at 10:03

Solution 1

$$\frac{111-11}{.1}$$

Solution 2

$$\frac{111}{.111}$$

Solution 3

$$\frac{1}{.111-.11}$$

Solution 4

$$\frac{11}{.111-.1}$$

Solution 5

$$\frac{11-1}{.11-.1}$$

Solution 6

$$\frac{111-1}{.11}$$

• 1) I would not consider the negative signs you used in solutions 2 and 4 to be subtraction symbols. 2) Along with the first point, and adding in solution 6, solutions 2, 4, and 6 are not of "six different solutions" in the spirit of the forms A/B = -A/(-B). Jan 30 at 18:43
• @ hexomino -- Attention! Your solutions 3 and 4 equal -1,000. Jan 30 at 18:50
• @OliveStemforn Apologies on 3 and 4, edited now. Sorry, also, my understanding of "subtraction symbol" was that negation was okay, my mistake. Jan 30 at 18:56
• hexomino, you have essentially three different solutions out of the six different solutions in your solutions 1, 3, and 5. There are still three other solutions significantly different from those that I am looking for from any contributor(s). Jan 30 at 19:14
• @OliveStemforn I've replaced 2, 4 and 6 now with something essentially different Jan 30 at 19:25