Monday, 13 May 2013

NG 126

New game 126 is now available.  Also, the MUMS Puzzle Hunt is on this week, so it's very likely my writeups will be late, possibly by the entire week.

Round 1: T S N I E R I A T

Ooh, another retsina mix so soon; I had TINS, TINES, SINTER ("Metallurgy to bring about the agglomeration of particles of a metal [...] by heating [...] to just below the melting point of the substance [...]"), RAINIEST, NITRATES, and a slightly uncertain TERTIANS (TERTIAN as a noun: "a tertian fever or ague [...]", where TERTIAN as an adjective is "recurring every other day, or, if considered inclusively, every third day").

After time I added NITRITES as another eight, and checked up on TRAINSET but was not surprised that it was not listed.

The other eights are STRAITEN ("to put into difficulties, especially financial ones") and INTREATS (INTREAT being an archaic variant spelling of ENTREAT) / INERTIAS.

My selection: NITRATES

Round 2: N O I I GW B A D


The other sevens are WINDBAG and GONIDIA (plural of GONIDIUM: "an algal one-celled asexual reproductive body, as a tetraspore or a zoospore").

My selection: ABIDING

Round 3: Target 192 from 25 100 3 1 9 7

I started in overly-complicated fashion with 192 = 100 + 3*25 + 9 + 1 + 7.  I knew the factorisation 3*64, though, and wanted to use that somehow; a little playing around produced 192 = (9 + 7)*(100/25)*3.  Another approach was 200 - 8, which I managed to make work with 192 = 100 + (7 - 3)*25 - (9 - 1).  Finally (and still within time!) I saw another way to make the 64 and bypassed the large numbers entirely with 192 = (9*7 + 1)*3.

My selection: 192 = (9*7 + 1)*3

Round 4: M D F O E U M M E

I had DOME, FUMED, MODEM, wondered about FEMDOM and FEMDOMME but thought (correctly) that they would not be listed, and MUMMED (MUM as a verb: "to say 'mum'; call for silence"; also, "to act as a mummer" -- a MUMMER is "someone who wears a mask or fantastic disguise, especially as formerly at Christmas and other festive seasons").  I flirted with MEMOED as another possible six but it does not get the nod from the Macquarie.

MUMMED is the only six; the other fives are ODEUM ("a hall or structure for music or dramatic performances") and FEMME ("a woman").

My selection: MUMMED

Round 5: H C R I E K A A R

I had RICH, HICKER (taking excessive advantage of the single-syllable rule for adjectives), wondered about HACKIER but thought it unlikely (indeed, it is not listed), HACKIE, ARCHER, HACKER, rejected CHAIRER (rightly), wondered about CHARIER (comparative of CHARY: "careful; wary"), was also uncertain about HIRECAR (which is listed, as it turns out, but only as two words), and a further dubious HAIRCARE (not valid).

Lots of ways to go wrong in the quest for more than six, so I was particularly pleased afterwards that my choice of CHARIER was the only right one.

There's several other sixes, of which I'll just mention CHAKRA ("(in yoga) one of the six (or seven) major centres of spiritual power in the body [...]").

My selection : CHARIER

Round 6: Target 899 from 4 7 7 8 3 6

A tough target for a six small mix; my usual technique for such is to divide by the largest number to get an approximate result.  In this case the target is 8*112 + 3, which seemed promising given that 112 is 7*16.  I was not able to make the 16 without using up the 3, though, and the best I managed from this idea was a one-away 900 = (7 + 3 + 6)*7*8 + 4.

I found a few other ways to 900 within time (such as 900 = 6*(7 + 8)*(7 + 3)), but did not write them down.  Somewhat after time I finally found the factorisation 29*31, and in retrospect that should have been obvious -- this is just realising that 899 is the difference of two squares (30^2 - 1^2) = (30 - 1)*(30 + 1).  A little work was able to produce both of those components, giving what turns out to be the only solution: 899 = (6*4 + 7)*(7*3 + 8).

My selection: 900 = (7 + 3 + 6)*8*7 + 4  [1 off]
Best: 899 = (6*4 + 7)*(7*3 + 8)

Round 7: S D N U A O T G E

We had a very similar mix recently in NG 121 (which had a P instead of the D).  Sevens galore, here.  I had SAND, SOUND, ASTOUND, OUTAGES, TONGUES, DONATES, and SOUTANE (a cassock).  After time I found UNSTAGED but was disappointed it is not listed, and noted other sevens of AUGENDS (AUGEND: "a number to which another number, the addend, is added") and SONDAGE ("a deep, narrow trench, showing the stratigraphy of a site").

Seven does seem the best on offer; the others are TONGUED, NOUGATS / OUTSANG, ONSTAGE / TANGOES (per David's ruling in episode 405, but Chambers would not allow it), SNOUTED (SNOUT as a verb being an obsolete colloquialism for "to rebuff"), TANGOED, and possibly DOTAGES if it may be pluralised.

My selection: ASTOUND

Round 8: Target 526 from 6 9 6 10 8 4

This was a much easier application of six small numbers; using the approach suggested in the earlier round, I wanted to get close to 53 and then multiply by 10.  I started with 526 = 6*9*10 - 8 - 6, then found another option in 526 = (8*6 + 4)*10 + 6.

My selection: 526 = 10*9*6 - 8 - 6


I had a detour here via -IEST, but saw the -NESS fragment soon enough.  I got slowed down by trying for -INESS (which is common enough as an ending), but once I got off that I found INEPTNESS without much further difficulty.

My selection: INEPTNESS (7.3s)


Victor said...

3. 192 = (9 - 7)*(100 - 3 - 1)
6. 3-away: 896 = 7*8*(7 + 3 + 6)
8. 526 = 6*9*10 - 8 - 6
9. INEPTNESS - 19.2s

Mike Backhouse said...

Here are mine:

(7*9+1)*3=192 (unusual for me to only use smalls but saw it was divisible by 3)
7*7*6*3+8=900 (1 off) - about 40s
SOUND (pity there is no word SOUNDGATE)
Victor's way
x- jumped in immediately with SPINSTERS. No R. After time looked for the -NESS word but did not see it.

Sam Gaffney said...

Nice smallwork, Mike, even if one was late.

3. 192 = 100 + 3*25 + 9 + 7 + 1
6. 1-away: 898 = (7*7*3+4)*6 - 8
8. 526 = 6*9*10 - 8 - 6
9. INEPTNESS - 3.9s

Geoff Bailey said...

Yes, nice work with the small numbers, Mike, but I have to pull you up on a couple of counts: That after-time computation for round 6 actually tallies 890. Also, there's only one N available for round 2, alas.

Victor: Did time get to you on that second numbers round? Adding the final 4 would have got you to one off. Solid results otherwise, and similarly for Sam.

My results:

3. 192 = (9*7 + 1)*3
6. 900 = (7 + 3 + 6)*8*7 + 4 [1 off]
8. 526 = 10*9*6 - 8 - 6
9. INEPTNESS (7.3s)


[4] To MUM is either "to say 'mum'; call for silence" or "to act as a mummer". A MUMMER is "someone who wears a mask or fantastic disguise [...]"

[5] I was very happy to successfully negotiate the various invalid options that I saw and choose the valid one. HACKIER, CHAIRER, and HAIRCARE are not listed, and HIRE CAR is two words.

[6] Much, much later I found the factorisation 29*31. This should have been obvious from the start as 900 is the square of 30 so 900 - 1 is the difference of two squares. Anyway, realising this enabled me to find what turns out to be the only solution: 899 = (3*7 + 8)*(6*7 + 4)

Sam Gaffney said...

I had wondered about MUMMED, but didn't take HIRECAR seriously.

A cool eventual 899 solve. By coincidence, I had been thinking only yesterday that the difference of two squares is the only element of post-primary-school mathematics even vaguely relevant to the numbers rounds.

Victor said...

Yes Geoff, time got me on that second numbers round - in fact I probably went about 3 seconds overtime scribbling the answer down.

I had also toyed with MUMMED and HACKIER, wasn't feeling like taking risks this time though.