Richard talks with Norm a little about how Norm helps train students for the mathematical olympiads. As Norm says, it basically involves feeding them maths problems and letting them go at it. I'll note from personal experience that there is a lot more done in the way of teaching and discussion about the problems, but fundamentally that is the approach: Get students working on challenging problems, see what they make of them, and then suggest ways in which they might find more helpful approaches to them.

Tonight's challenger is Gavin Griffith, a primary school teacher. Seven years ago Gavin "stumbled upon" a sports camp in America, and since then has spent pretty much every American summer there (from about May through to September), dealing with around 260 kids playing a variety of sports. As Richard points out, this means that Gavin more-or-less gets a perpetual summer, or at the very least avoids winter. The camp involves a lot of team sports; Gavin says that he isn't that good at the sports but makes sure that they play safely and have a good time.

Norm gets an early lead due to a longer word and an error from Gavin in the numbers. Gavin misses a couple of chances to create longer words by prefixing in the next two letters rounds, thereby giving up seven points instead of gaining them. Norm makes a mistake in the second numbers round to give some of the large lead back, but manages to ride his remaining eleven point lead into the conundrum for safety. Once again Norm solves it, a bit short of halfway, to end up winning 61 to 40.

I had a very disappointing night tonight. Two words turned out to be invalid (I didn't get any longest word within time) and I was uncomfortably far away on one numbers round. It was a night for seeing better answers within five seconds of time running out, which is always a bit frustrating. I was actually behind going into the conundrum, but honestly fortunate to still have a chance by that point since it needed Norm's error to bring me back into contention. I solved the conundrum quickly to escape with a very lucky win, perhaps making up for some poor luck in the game.

**Round 1: S I B N A D E T D**

I had BINS, BANDS, BASINED, BASINET, DETAINS, wondered about BANDIEST, and DISBAND. Just after time I added DANDIEST. I would have been very happy to declare DANDIEST if I'd seen it in time, but BANDIEST caused me some concerns. I eventually decided to risk it, and it turns out not to be listed.

In retrospect this was a poor decision since BANDY doesn't really refer to a concept that maps well to comparative/superlative extensions. Had I the luxury of a lot of time to decide which word to declare I might eventually have gone the correct way; but I already probably take more time than I should over this.

Both contestants have chosen some of the many sevens; Norm has INSTEAD while Gavin has BANDITS. David has DANDIEST for his eight; he wishes that Norm had chosen a final vowel as an A would give ABSTAINED. (An O would have also allowed BOTANISED / BASTIONED.)

There's almost another eight here, but the Macquarie insists that SIDE BAND is two words; I don't think that reflects contemporary usage at all well, quite frankly.

Norm: INSTEAD

Gavin: BANDITS

Me: [invalid]

David: BANDIEST

Scores: Norm 7, Gavin 7, me 0

**Round 2: R L M A U E K C S**

I had MARL, MURAL, REALM, wondered about MUCKLES, SUCKLE (I knew from my match against Brett that SUCKLER would not be valid), SCREAM, and SLACKER. After time I added MUCKERS, and checked on MUCKLE to find out that it is listed as an adjective (synonymous with MICKLE, meaning large or great) so MUCKLES would not have been valid.

This time Gavin's choice of MURALS is outdone by Norm's choice of MAULERS. David mentions SLACKER for seven, but has found CAULKERS for eight. He also points out that the first vowel was the A that he'd wanted for the previous round.

That does seem to be the only eight; there are a fair few sevens but I'll only mention a couple. MACKLES because it is an interesting word (MACKLE: "a blur in printing, as from a double impression"; it is also a verb, opening up MACKLED and MACKLING, and has the alternate spelling MACULE -- thus MACULES is also valid here), and RECUSAL / SECULAR because that seems like a relatively common letter mix to arise.

Norm: MAULERS

Gavin: MURALS

Me: SLACKER

David: SLACKER, CAULKERS

Scores: Norm 14, Gavin 7, me 7

**Round 3: Target 970 from 50 9 5 3 6 9**

Looking at the available values, my first thought was to get there as 1000 - 5*6. Unfortunately I could only make the 1000 by using up them both, and I ended up three away with 973 = (9 + 6 + 5)*50 - 9*3. I wasted a lot of time on unprofitable lines of thought, sadly. After time I found several ways to 972, but then paid a bit more attention to my original idea. Since 1000 is divisible by 5 this is classic tweakage territory, and a solution follows pretty easily once it is considered in this light: 970 = 5*(50*(3 + 9/9) - 6). So near, and yet so far...

Both contestants have also declared three away, in different directions, so at least I've not lost ground. Norm used the same method that I did to get 973, but Gavin has declared 967 with (9 + 6 + 5)*(50 - 3). That is 940, of course, and his answer is invalid. What I believe happened here is an easy enough oversight: He multiplied that 3 by (6 + 5) only, dropping the 9 component. A shame, and that puts him in danger territory at 14 points behind.

Lily is as reliable as ever, showing the solution that I mention above; it turns out that this is the only one.

Norm: 973

Gavin: [invalid]

Me: 973

Lily: 970

Scores: Norm 21, Gavin 7, me 14

**First break: DREW FOUR ("Of brow and plough")**

A nice double association for FURROWED.

David's talk is about the phrase "to read someone the riot act"; he starts out by reading the original text of the actual act in question.

**Round 4: N H L O I A O T R**

I had LION, HALON, LOTION, ORATION, and then was pleased to see LOTHARIO. This, I felt sure, would turn the game around for me.

Both contestants have settled on sixes: Norm with LOTION and Gavin with RATION. David points out that Gavin could have simply prepended an O to get ORATION for seven; he then says that LOTHARIO is in the dictionary... but only listed with a capital letter. He says that would have been a real booby-trap (a mild pun on the ladies' man meaning of LOTHARIO) for some players. How very true, alas.

David has found the only eight, though: HORNTAIL, a type of wasp.

The other sevens here are HORNITO ("a low oven-shaped mound, common in the volcanic districts of South America, etc., usually emitting hot smoke and vapours from its sides and summit") and ORTOLAN (a bird; either a type of bunting, or another name for the bobolink).

That second invalid word puts me in deep danger territory at 14 adrift. Had I settled for sevens each time I would have been six ahead at this point.

Norm: LOTION

Gavin: RATION

Me: [invalid]

David: ORATION, HORNTAIL

Scores: Norm 27, Gavin 13, me 14

**Round 5: C A M O R E B S I**

I had COMA, CAROM, CREAM, CAMBER, CAMBERS, CORBIES (I mentioned this in episode 401, just two days ago), and ASCRIBE. Just after time ran out I saw MICROBES, to continue the sense of frustration.

Norm has COMBERS, beating Gavin's choice of SCRIBE; once again David points out that just prepending a vowel would have given Gavin a longer word; in this case, ASCRIBE. That's 14 points of turnaround that could have been generated on these two rounds by that method.

David has found MICROBES and AEROBICS for eight.

Another possible eight is CRAMBOES (CRAMBO: "a forced rhyme"), but I'm not sure what the position would be. The show's rules on regular inflected forms (taken from the Macquarie's preface) indicate that a plural formed by addition of -S or -ES does not need to be listed. It does not cover the question of which is acceptable in which cases; presumable TALKES would be rejected as the wrong way to pluralise TALK, for instance, but to do so is resorting to information from outside the dictionary.

So what does it mean that CRAMBO does not have a plural form explicitly listed? One ruling might be that only CRAMBOS is valid; if so, why does NACHO explicitly list the plural as only NACHOS? So perhaps only CRAMBOES is OK... but then POTATO explicitly lists the plural as only POTATOES. So it must be that the lack of a specified plural means that both are OK... but then ZERO explicitly lists both ZEROS and ZEROES. There's a fundamental lack of consistency about this!

In contrast, my Chambers 20th Century dictionary has a very good section at the front where they lay out their general rules for inflected forms. In particular, there is a brief mention that the default position is for nouns ending in

*o*to simply add

*-s*to make the plural; they then point out a few exceptions, both cases where adding

*-es*is correct, and cases where either form is acceptable. They round it off by stating that such cases will be indicated in the entries. This is the kind of explanation and consistency that the Macquarie could really use, quite frankly, and I hope a later edition gets something similar.

Oh, and Chambers lists CRAMBOES as the plural form. I don't think the show has much ground for ruling out either CRAMBOS or CRAMBOES, however; but all in all, it's not a good risk to take if there's an alternative.

I'm still more than a conundrum behind, and the numbers rounds can sometimes be so easy that there's no chance for gain. There's a serious risk that I'll lose this game before the conundrum.

Norm: COMBERS

Gavin: SCRIBE

Me: CORBIES

David: ASCIBE, MICROBES, AEROBICS

Scores: Norm 34, Gavin 13, me 21

**Round 6: Target 575 from 25 1 9 6 9 10**

The target is a multiple of 25, so there's every chance this will be easy. The required multiple is 23, and so I have 575 = 25*(9 + 9 + 6 - 1) in short order. I also note a couple of ways to use the 10 and 25 to get there: 575 = (9*6 + 1)*10 + 25, and 575 = (9 + 1)*6*10 - 25. Just now I have seen how to avoid the 25 entirely, with 575 = 9*(9*6 + 10) - 1.

Both contestants say that they think they got there; I'll note that Norm was writing up until the very end. Gavin demonstrates the first solution that I mention above -- this was also used by Lily -- but Norm has apparently made a mistake. He says it was supposed to be the same as that one, so presumably he had a transcription slip somewhere. Unfortunate for him, and very fortunate for me and Gavin.

Norm: [invalid]

Gavin: 575

Me: 575

Lily: 575

Scores: Norm 34, Gavin 23, me 31

**Second break: AIRY MUTT ("By virtue of age")**

A reasonably stright reference to MATURITY.

**Round 7: R E T A P E N S U**

I had TEAR, APTER, PARENT, PARENTS, and wondered about PRETUNES. Eventually I decided that I'd had enough of declaring invalid eights for the day and stayed with PARENTS, which turned out to be the right choice. I have to say that my mood would have been rather grim if I'd declared a third invalid word tonight!

It's PARENTS from Norm and REPEATS from Gavin. David says that there are many sevens (certainly true!), mentioning TUREENS / NEUTERS before he reveals his eight: SAUTERNE.

That's the only eight to be had, and completes a perfect game from David. All letter rounds have had an eight as their best, and in four of the five cases there has only been one. Great wordwork from David tonight!

Some online sources do list SUPERNATE as a synonym for the noun sense of SUPERNATANT. However, the Macquarie only lists an adjective sense of SUPERNATANT so there is no full monty here.

Norm: PARENTS

Gavin: REPEATS

Me: PARENTS

David: TUREENS, NEUTERS, SAUTERNE

Scores: Norm 41, Gavin 30, me 38

**Round 8: Target 858 from 100 4 9 1 5 3**

I can still lose the game here, but even with an optimal result I'll still need the conundrum to ensure a win. Disappointing to be in such a position so early in the series. Gavin needs to gain points over Norm here in order to have a chance; perhaps a single large number is not the best strategy in such circumstances, but it depends on how comfortable Gavin is with the numbers.

The target is 42 away from 900, and a little tweakage seems indicated. I had 858 = 9*(100 - 5) + 3. A relief to know that I'll have a chance after all!

Both contestants have solved this; Gavin has also done it that way, as has Richard, it turns out. But Norm has instead chosen 858 = 9*100 - (4 + 3)*(5 + 1); this was also Lily's approach.

That means Norm will win -- although possibly only by a single point if Gavin solves the conundrum.

Norm: 858

Gavin: 858

Me: 858

Richard: 858

Lily: 858

Scores: Norm 51, Gavin 40, me 48

**Round 9: LOSER CASE**

The one thing I'm particularly on edge about with this round is that Gavin might turn out to be a conundrum whiz. If he gets it first then I lose by default, which would be annoying... although since he would then overtake me, it would also be fair enough.

The words are revealed and I'm hoping they don't turn out to describe my results... then I see the answer just over a second in. Phew! Norm continues his good conundrum solving form by also seeing it, at around the thirteen second mark or a little after.

Norm: CASSEROLE (13s)

Gavin: [no answer]

Me: CASSEROLE (1.5s)

Final scores: Norm 51 (61), Gavin 40, me 58

Gavin could have really worried Norm here if he had found those seven-letter words in rounds four and five; and much more so if he had managed better in that first numbers round. Aside from that it was a decent standard of play from both contestants and certainly Gavin gave Norm the biggest challenge he has yet faced. Norm gets another score in the sixties and is currently averaging exactly 62 points a game. Based on last series' performances, even if Norm loses his next game he should make the final.

I'm obviously pretty disappointed in my results today, with two invalid words and a numbers round I should have done better on. I did not manage a single maximum on the letters; that's a big drop from yesterday where I managed four out of five. In the end I was lucky that Norm made that error which allowed me back into the game, and that's never something one would want to rely on.

Still, there's always another chance; I'll be hoping to do better tomorrow!

## 5 comments:

1. BANDITS

2. MAKERS

3. -

4. ORATION

5. CREAMS

6. -

7. PARENTS

8. 860 = 9*100 - 4*5*(3-1)

9. Didn't have it by the time Norm said the answer.

Definitely need to work on my numbers skills!

You were rather unlucky tonight Geoff, but nice fast conundrum.

Nice work on ORATION, Mark. If you are concerned about numbers performance, you will find that practice helps enormously (including practising the writing-down of answers, though it doesn't have to be every time). If you are keen, a good tool is here:

http://www.crosswordtools.com/numbers-game/

I was a little annoyed with BANDIEST not being listed in the Macq, as I remembered that BANDY was an adjective. I saw DANDIEST well within time, but thought that I'd already seen BANDIEST before.

I paused the game when Lily said she got to 970 and got the answer quite quickly. It's a bit of a risk when you are chasing a number to multiply that is so far above 100 (in this case 194), because you lose precious seconds calculating the subtotal to chase, and if you can't hit it, you can be left with nothing. This happens regularly in six-small selections with high targets, you have to pick a number to divide the target by early on and then hope that everything works out.

I was very tempted to declare SUPERNATE, thinking SUPRANATE was a word (it isn't, I probably got confused with SUPINATE).

My answers:

- (BANDIEST)

SLACKER

972 = (9+9)*(50+5) - 6*3

ORATION

COMBERS

575 = (9+9+6-1)*25

REPENTS

858 = (100-4)*9 - 5 - 1

1.25 s

Some good words there from you Mark, particularly ORATION. With the first two numbers rounds, and particularly with the single large number mix which lends itself very well to this, you may find that what I've been calling the "standard method" might help you.

The idea is to use whatever large numbers are around to get near, or as near as easily possible, then use the remaining items to adjust. In the case of the first mix, we are looking for multiples of 50, so the first step is to divide by 50 and see that we want to get either a 19 for 950, or a 20 for 1000.

The small numbers aren't the most flexible, but finding 9+6+5 for 20 from them is manageable. That then leaves the 9 and 3 around in order to get closer, leading to the 973 that Norm and I had.

In the second mix, the target is a multiple of the 25 that we have. So it becomes a question of making the 23 from the rest, and again this turns out to be fairly manageable. It's OK to take a while to work out the division; a helpful shortcut for 25 is that each multiple of 100 counts as 4, so 575 is 500 + 75, leading to 20 + 3 = 23 as the multiplier. (Alternatively, it is 600 - 25, giving 24 - 1 = 23.)

You were pretty close on the final one! Norm and Lily showed how one might get the requisite 42 from the remaining items. The other option is tweaking a bit -- since you're already using a 9 to multiply, you can get to use it again if you multiply also. (I hope you see what I mean by this.)

Since the small numbers were at the small end, small adjustments were always likely to be easy which is another hopeful sign for tweaking since it often leaves you a little away from the target. In my case, I saw that the difference was 42, and the nearest multiple of 9 was 9*5 = 45. We had both the 5 and the remaining adjustement of 3, and my solution (and Gavin's!) dropped out directly.

The numbers rounds are actually the easiest part of the game to train, or so I feel. With practice the multiples of 75 (etc.) migrate to just being known, and you learn techniques like how to tweak effectively. (In contrast, most of the effort in the letters rounds is in having a large vocabulary, something that takes years to develop.)

If you do end up practicing, one thing that I recommend is to abandon the time limit. Work on a problem until you are satisfied with your answer, or that you are not going to see better for some time. If better does turn out to be possible then you may well see either a new technique, or how you might have found it if you had tried a particular approach that you already knew.

(This applies to the letters rounds as well, incidentally. And arguably the conundrum as well. Train to get an answer, and speed arrives in due course.)

Thanks, Sam. I wasn't quite fast enough, though. :)

Also, Tim: This post's rant about the Macquarie was for you.

Sam, thanks for the suggestion. That website looks very useful.

Geoff, thanks for your detailed explanation of numbers techniques. The "standard method" is essentially what I try to do, although I think I'm less systematic because I haven't been dividing at the start to work out what factor I need. Thanks also for the advice about practice.

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