Listener Crossword 4190

[crosswhit99]

Have identified the eight nets of cubes but now am struggling with the next step. Someone suggested I make models of the eight cubes but I have OA and this is a non-starter unfortunately. Any suggestions how to proceed please - thanks in advance !

[Mysterons]

You might find it helpful crosswhit to convert all 8 cube nets to the same shape - I chose the cross and placed the 5 at the centre. Then considering in isolation the two small cubes that form the junction between the large cube faces bearing 5s and 2s, there are only six "possible" combinations (determined by the need for the touching face between them to match) from the 6 cube nets available (2 are unavailable as 5 and 2 are on opposite faces). Only 2 of these "possible" combinations can lead to a completed large cube having all internal faces matching, and these 2 large cubes have the same net.

[crosswhit99]

Thanks for the pointer Mysterons - I'd overlooked that the 5 and 2 must be on adjacent faces

[sohcahtoa]

I have completed the grid but can't find the "cubes". Have I gone wrong with the numbers - I have several 7s, 8s and 9s - is this possible? Please help.

[Mysterons]

Yes, there are 8x8 = 64 cells in the grid, but only 8x6 = 48 are occupied by the digits 1 to 6 (eight of each). There are also seven 7s, six 8s and three 9s. So there are exactly enough cells to make eight cube nets, with only one possible layout.

To get started finding the nets I suggest you start in the cell numbered 37. Check which of the three adjacent cells could be part of the same net, and shade the two cells the same colour. Then repeat the process for the other three cells around the second cell, but this time just note the possibilities, as you could go down the wrong track. However, it soon becomes apparent that there is only one way to obtain six contiguous cells with different digits.

Then repeat the process with a different colour ....

[sohcahtoa]

Very many thanks for your reply. At least I know I am on the right track so will keep plodding.

[saladdodger]

I have a full grid but can't find a net (non-conventional )to include my 5 (at the end of 8d) . The 2 up and left from it can't be in the net because it would then be conventional; If I take the 2 from down and left of the said 5, then I am left with a 3 from 8d which I can't fit in anywhere. Any advice please? (beside give up!) Thank you

[Mysterons]

The 2 above and to the left is in the same net as that 5 saladdodger - in fact if your grid fill is correct it should be impossible to place these two cells in a conventional net.