private void CheckEveryOther_Click(object sender, System.EventArgs e) {
    // Cycle through every item and check every other.

    // Set flag to true to know when this code is being executed. Used in the ItemCheck
    // event handler.
    insideCheckEveryOther = true;

    for (int i = 0; i < checkedListBox1.Items.Count; i++) {
        // For every other item in the list, set as checked.
        if ((i % 2) == 0) {
            // But for each other item that is to be checked, set as being in an
            // indeterminate checked state.
            if ((i % 4) == 0)
                checkedListBox1.SetItemCheckState(i, CheckState.Indeterminate);
            else
                checkedListBox1.SetItemChecked(i, true);
        }
    }        

    insideCheckEveryOther = false;
}