An Old Ruler

Geometry Level 2

Chris has an old 6-inch ruler that is missing the 4 in4 \text{ in} mark. However, he can still measure all integer lengths from 1 in1 \text{ in} to 6 in.6 \text{ in}. He'd like to see if he can erase more marks and still be able to measure all integer lengths from 1 in1 \text{ in} to 6 in.6 \text{ in}.

What is the minimum number of marks the ruler could have?

Chris' ruler can measure all integer lengths from \(1 \text{ in}\) to \(6 \text{ in}\) with only 4 marks. Chris' ruler can measure all integer lengths from 1 in1 \text{ in} to 6 in6 \text{ in} with only 4 marks.

Note that all measurements must be made directly using the ends of the ruler and/or its marks. For example, you can't repeatedly use a distance of 1 in1 \text{ in} to make larger distances.

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