Create number list for a second cell based on number selected in first cell

I apologise if this is not a formula/function problem.

I want users to select a "low" number from a drop down list in G2
(I have set this up using data validation using a named range that includes the numbers 1 through 12)

Then I want the user to select a high number from a drop down list in G3

Is it possible to force the drop down list to only include numbers equal to, or greater, than the number selected in G2 through to a maximum of 12
ie can I force a way for the choice in G3 to NEVER be less than the choice in G2?

Example 1:
In G2 the user chooses "3"
In G3 the user is presented with a drop down list of only 3, 4, 5, 6, 7, 8, 9, 10, 11, 12

Example 2:
In G2 user chooses "8"
In G3 the user is presented with a drop down list of only 8, 9, 10, 11, 12

I tried using dependent data validation but because the categories in G1 are numbers, I can't use the name of a range as a number
Perhaps there is a more elegant solution than my feeble Excel experience can think of?

Many thanks for any solutions/guidance.

Thank you for taking the time to answer.

The formula you provided only returns a single number? (I removed the ":Sheet1!$K$13" as it returned a #VALUE! error ... but maybe I misunderstood)
I tried using it as the rule in the data validation dialogue box and got this error:
Snap_2018.05.31_23h45m58s_003_.png


I need G3 to show a list of numbers that the user can choose from (value in G2 up to and including 12)

"create a new named range which the validation rule can refer to"
This is what I'm having trouble doing - I just can't get anything I try to work.

I have attached a new file with the results I need in the drop down list (G3) for each option in G2
I'm sure I'm not setting up this table correctly, not naming it correctly and not using the correct syntax/formula in the data validation for G3

Again thank you for you help.
Still hoping for a solution.