This is a tough game that requires making some key inferences in order to tackle it within a reasonable amount of time. I think that the biggest inference to be made is that the game board is multi linear with 2 spaces each over 4 slots. We also have an HJ block.
Immediately, that means that the HJ block can be placed in one of three ways. Slots 1 and 2. Slots 2 and 3. Slots 3 and 4.
If we place HJ in slots 1 and 2, we can work the game out while abiding by the other rules.
If we place HJ in slots 2 and 3, then J and O are together. If J and O are together, where can G be placed? Considering neither J nor O can repeat, G would not be able to go anywhere on the diagram, meaning that HJ in slots 2 and 3 is not a possibility.
If we place HJ in slots 3 and 4, then H and O are in together in slot 3, while J is in slot 4. This forces G into slot 4 with J (it needs to be with either J or O). Considering that one of the variables in slot 4 must repeat, and that J cannot repeat because it carries H and G cannot repeat because it would carry another O or J (which themselves cannot repeat), then this configuration cannot work either.
This is how we know that HJ must be placed in slots 1 and 2 respectively. It is the only possibility for these variables.
I hope this was helpful. Please let me know if you have any other questions.
