Entry#4 Great start! Like how Greek and 123 is presented and how you trademark/slogan was incorporated underneath. I would suggest making less "children" like as we offer to all ages.
Entry #10 Nice design. The font is simple and sharp. The slogan is used effectively. In addition, the 123 tells you something. Not too crazy about the gradient shading in the work Greek.
Entry #43 and others. Can you please make the slogan larger? to occupy the logo perhaps from left to right? Concern it is still far too small. Thank you
Entry#42 Can you give entire design a thicker stroke? There is concern within company that design is too thin and does not fit design of website. Making text Greek and also 123 thicker would make it match up a lot more.. perhaps.