NG 108

New game 108 is now available.  Apologies, once again I had everything ready to go and simply forgot to enable it before I left.


Round 1: A O I E S C F P R

I had ICES, FACIES ("a general appearance of something naturally occurring, as a particular flora, fauna or ecological community"), and COPIERS.  After time I noted other sevens of SCRAPIE (a disease affecting sheep and goats) and FORCEPS.

It turns out I was close to the eight there -- the only eight appears to be FORCIPES, one of the plural forms of FORCEPS.

The other sevens are PROSAIC / PICAROS (PICARO is a variant spelling of PICAROON, which I mentioned recently in NG 104: "a rogue, thief, or brigand"), SOAPIER, SCORIAE (plural of SCORIA: "the refuse, dross, or slag left after smelting or melting metals"), and FIACRES (FIACRE being another term for a hackney-coach).

My selection: COPIERS
Best: FORCIPES


Round 2: T T L T I E I E N

I had TILT, TITTLE ("a dot or other small mark in writing or printing, used, for example, as a diacritic"), and ENTITLE.

That looks like the only seven; the other sixes are NETTLE / TELNET ("a program for opening a shell (def. 20) on a remote computer").

My selection: ENTITLE


Round 3: Target 828 from 100 75 25 50 5 1

The target is very near 11*75 = 825, which seems like the obvious place to start.  That led me to two away with 826 = (5 + (100 + 50)/25)*75 + 1.  Switching tacks I found two away on the other side with 830 = 5*(100 + 75 + 1) - 50.

It turns out that the target is unreachable, but it is possible to do better.  There's a single way to get one away, which I might have found but it hit one of my blind spots: 829 = (50/5 + 1)*75 + 100/25.  Dividing 50 by 5 to get the 10 makes the 11 more cheaply, and that would be a well-deserved optimal result from anyone who spotted that.

My selection: 830 = 5*(100 + 75 + 1) - 50
Best: 829 = (50/5 + 1)*75 + 100/25


Round 4: R B H T A N E I N

I had BATH, BREATH, ENTRAIN, and HAIRNET.  I observed that a final vowel could have been another E to yield HIBERNATE / INBREATHE, but it turns out that the next vowel was an O so this was not on the cards (although a familiar BARITONE would have been).  After time I noted down THINNER as another seven.

Seven is the best to be done, and that looks like all of them.

My selection: ENTRAIN


Round 5: O O O T M R M K P

Bleah, a bad set of letters.  I had MOOT and MOTOR, and that was the best to be done.

The other fives are TROOP, TROMP, and PROMO.

My selection: MOTOR


Round 6: Target 513 from 25 8 6 3 1 4

I recognised the target as 8 cubed plus 1, but the factor of 9 seemed more provocative.  The cofactor is 57, and luckily I set the 6 and 3 aside to make the 9 instead of 8 and 1.  That made it easy to find 513 = (8*4 + 25)*(6 + 3).  On the other hand, if I had set aside 8 and 1 I might have found (as I have seen just now) the alternative solution 513 = (25 - 6)*3*(8 + 1).

Looking at the standard method, the offset of 12 is generally better than 13, and in this case could be either 3*4 or 8 + 4.  That led me to an alternative solution of 513 = 3*(6 + 1)*25 - 8 - 4, although the tweak of 513 = 3*((6 + 1)*25 - 4) would have been cleaner.

My final effort (still within time!) was to revisit that idea of 8 cubed plus 1; 8 cubed is 8*64, which is 8*4*16, and that fortunately worked out: 513 = 8*4*(25 - 6 - 3) + 1.

My selection: 513 = (8*4 + 25)*(6 + 3)


Round 7: A E E C S S G H E

I had CEASE, CEASES, GASHES, and CHEESES.

CHEESES looks like the only seven.  The other sixes are CHEESE and CASHES / CHASES / CHASSÉ ("Dancing a kind of gliding step in which one foot is kept in advance of the other").

My selection: CHEESES


Round 8: Target 439 from 5 7 4 3 10 3

My first instinct here was to divide by 3 as an approximation, but I did not end up investigating that much.  Instead I looked at dividing by 7 and got to two away with 437 = (5*10 + 3*4)*7 + 3.  Then I tried dividing by 10 and that got me to one away with 440 = 10*4*(5 + 3 + 3).  But it was looking at working up from 420 (arguably as a result of dividing by both 7 and 10) that led me to find a suitable tweak: 439 = (3 + 3)*(7*10 + 4) - 5.

To break down the reasoning for that last, I had seen that I could get to 420 via (3 + 3)*7*10, which left the 4 and 5 available -- providing another way to one off, incidentally, with 440 = (3 + 3)*7*10 + 4*5 -- and the question was if those could be used to make 19 instead of 20.  The answer was that 4*6 - 5 = 19, and hence the previous solution.

After time it became clear that I had rather overcomplicated matters: Working down from 450 was much easier, yielding the solution 439 = 3*3*5*10 - 7 - 4.  Heh.

Later searching showed that there are only two other solutions.  Another way of viewing the solution that I found is that it is 444 - 5, where the 444 was made as 6*74.  This could have been broken up instead as 12*37, leading to the solution 439 = 3*4*(3*10 + 7) - 5.

The other solution gets back to the original plan of dividing by 3: 439 = (7*5*4 + 3)*3 + 10.

My selection: 439 = (3 + 3)*(7*10 + 4) - 5


Round 9: PARK BECAP

The word BECAP is not in the Macquarie, but I wanted to present the letters in the order that I was given them.  (Also, there were not many options for dividing the conundrum up without giving the answer away.)  Once I pulled out the -ACK fragment it was not too hard to find PAPERBACK.

My selection: PAPERBACK (4.0s)