-
Yes, that was what my first set was like.
Actually being too cheap to buy any more tyres for a while, I've stuck a thick puncture repair patch on the inside of the tyre under the cut and this seems to have sorted it. The last time I tried this failed totally, but I went to a bit more effort cleaning up the inside of the tyre first this time and it held without any issues for the whole of the ride I did yesterday.
On the other hand I've pretty much run out of patience with G-One speed 30c (I think - their tyre naming is so confusing). Ruined a nearly new one yesterday by rolling over a piece of glass at end of my road. Which is the second one in a row that's not lasted more than a few rides. Don't know if they changed the compound or something. My first set (when they were called S-Ones or something) lasted for ages.
The lesson is probably just not to ride bikes in the UK.