New game 76 is now available.
Round 1: E A T D G C A M W
I had DATE, GATED, ACTED, and DAMAGE. I also amused myself by noting MEGACAT, but obviously it was not a serious proposition.
It turns out that DAMAGE is the only six, and the best to be found.
My selection: DAMAGE
Round 2: N S N I M E E A F
I had INNS, MINES, FAMINES, NEMESIA (a type of plant that readers may recall from an appearance in episode 17), and FANNIES.
Seven looks like the best possible, with the other one being MEANIES (an anagram of NEMESIA).
My selection: NEMESIA
Round 3: Target 775 from 25 75 3 6 3 10
A sadly easy target; I went with 775 = 75*10 + 25 at first, then used the factorisation 31*25 to find the alternative 775 = (75/3 + 6)*25.
My selection: 775 = 75*10 + 25
Round 4: N T R E I M Z E E
I had RENT, INTER, MINTER (although I had to check later to confirm its validity), and ERMINE. I did wonder about METRIZE, but it is not valid (although METRIST is). A little later I came back and looked at it and saw EREMITE ("a religious solitary; a hermit") for seven.
There are two other sevens; TEENIER was findable, but EMETINE (an ingredient of ipecacuanha) was new to me.
But there is an eight: ETERNIZE (variant spelling of ETERNISE: "to make eternal; perpetuate").
My selection: ERMINE
Round 5: O P O R A S H I S
I had POOR, SPOOR, PARISH, and wondered about but rejected POORISH. That is listed in the Scrabble word list, but not in the Macquarie.
Once again, six is the best here. There are a few, of which I'll just mention SPOORS, SHARPS, and ARIOSO ("(a musical direction) in the manner of an air or melody").
My selection: PARISH
Round 6: Target 766 from 50 75 100 7 10 4
Neither offset (9 or 16) is obviously makeable, but then I spotted another option and found 766 = (75 + 100/50)*10 - 4. A little further thought found a way to make that offset of 9, though, with 766 = 7*100 + 75 - 50/10 - 4.
My selection: 766 = (75 + 100/50)*10 - 4
Round 7: O C E N E T B K E
I had CONE, CENTO ("a poem composed wholly of quotations from other authors"), KETONE (a type of organic compound), BECKET ("a loop or ring of rope forming a handle, or the like"), BECKON, and BETOKEN.
BETOKEN is the only seven; the other six is KETENE ("a highly reactive gas [...]"). The Macquarie does not list CENOTE, unfortunately.
My selection: BETOKEN
Round 8: Target 688 from 25 7 8 3 9 5
There's a couple of ways to make the necessary offset of twelve (7 + 5 and 9 + 3). While investigating ways to get to the required 700 I spotted one more option and a tweak saw me home: 688 = (25*7 - 3)*(9 - 5). Then I realised that the offset of thirteen was more manageable and found the option 688 = 9*3*25 + 8 + 5.
My selection: 688 = (25*7 - 3)*(9 - 5)
Round 9: NINE AXLES
I wasn't at all close to solving this; the answer is SEXENNIAL ("occurring every six years").
My selection: [no answer]