Games for PlayingAuthor(s): Alan ParrSource: Mathematics in School, Vol. 23, No. 3 (May, 1994), pp. 11-13Published by: The Mathematical AssociationStable URL: http://www.jstor.org/stable/30216465 .

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Games

F O R

Playing

Three Games by Alan Parr

V

In The Box In The Box is a very flexible game that I've used in lots of situations. In the form given I often use it in primary school staff meetings, where among other things it demon- strates that:

(a) a game can stimulate people to do willingly some quite demanding and not very attractive arithmetic,

(b) even when a calculator is available people's natural first approach to an arithmetical problem is a mental one,

(c) there are many circumstances when a good estimation is an appropriate response,

(d) a good activity may require little teacher input - I simply hand the sheets out without giving any instruc- tions, but such questions as "What's the maximum possible score?" are invariably raised,

(e) a game can stimulate people (even tired and cynical teachers!) to give repeated practice to skills of mental arithmetic - and then to do the whole thing all over again simply because they want to do better the second time around.

Perhaps the best thing of all about the game is its flexibility. You can use the identical presentation but with easier or harder numbers, or a different operation. You can ask pupils to combine three numbers rather than two, and adjusting the scoring system enables you to finetune the degrees of accuracy to exactly the level that you wish to see used.

Unfortunately I can't remember where I first came across this type of game, but the particular presentation used in the diagram is taken from that I used in the Hertfordshire booklet "The Calculator Collection". The booklet includes both the version shown here and also a blank grid for preparing your own versions. The booklet itself contains 26 pages of advice and ideas, and there are a further 12 photocopiable resource sheets. It costs a2.50 post free and can be obtained from Hertfordshire Education Services Publications, The Education Centre, Butterfield Road, Wheathampstead, Herts AL4 8PY.

Mathematics in School, May 1994 11

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IN THE BOX

15.2 10.6 0.4 26.2 7.05 41.9 58.99

60-87 22.4 34.43 16 27 99.9 18-03

47.7 81.3 0.091 66.6 0.87 0.45 0.1

37.6 59.2 5.86 9.14 73.2 6.41 3.27

Choose two numbers from the list (above), and add them.

Cover the numbers with a counter.

Find the box (below) for your answer.

Keep score of your points. The game lasts until all numbers have been covered.

The same number may not be used twice.

0-20 20-40 40-60 60-80 80-100

1 point 2 points 3 points 2 points 1 point

12 Mathematics in School, May 1994

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Lachaino 720

4

17160...

3

2

1

a b c d

'160

On a blank copy of the 4 x 4 grid shown in the diagram I've written the numbers 1-16 in a chain (all connections are made horizontally or vertically, so that there are no diagonal links). I then proceed to give you some clues about the positions of the individual numbers by telling you the products of sets of four numbers making up 2 x 2 groups of small squares. Can you deduce the entire chain?

In this case, clue A is that the four numbers in cells a3, a4, b3, b4 have the product 17160. Clue B: b2, b3, c2, c3 have the product 720. Clue 2: c2, c3, d2, d3 have the product 160.

Solving a Lachaino problem calls upon a lot of knowledge of factors and multiples. If the 4 x 4 grid isn't sufficient for you, you may like to know that I've played games using a 1-100 chain on a 10 x 10 grid - in this case a calculator comes in pretty handy when you're offered 29111040 as a helpful clue!

A good way of playing Lachaino is to use a Battleships or Mastermind format, where two players set problems for each other. Alternatively, the questionmaster may set the same problem to a number of individuals, who each make their own enquiries, so that the aim becomes to identify the chain in the smallest number of enquiries.

I'd also offer one final suggestion. Lachaino seems to cry out for a computer version, and I'd certainly welcome hearing from anyone who gets around to - or who primes a student to - writing such an implementation.

Footnote: Unlike many games, the history of Lachaino is well documented. A number of us, of whom Mike Taylor was perhaps most involved, tried out several versions before settling on the final form. Trial games involved additive versions, versions using negative as well as positive numbers, versions using chains solely of odd numbers and/or primes, and games with several interpenetrating chains rather than one long chain. In the final form we found that games on a grid as big as 10 x 10 are perfectly viable, and with best play seem to take between eight and ten enquiries.

Some Games With Numbers Here are a few unusual games with numbers. Some of them are sillier than others, but they offer scope for a variety of exploration and research, and like all good games

they're enjoyable as well. Many of them are enhanced by being played for a nominal prize - Fun-sized Mars bars may be suitable.

Milford Central is for a group of any size. In Round 1 each player chooses a whole number from 1 to perhaps 50 (inclusive). Anyone who chooses the same number as anyone else is out, but those who chose an unduplicated number proceed to Round 2. In Round 2 the surviving players choose any number which was not chosen (either duplicated or unduplicated) in Round 1; again, those who choose the same number as anyone else are out. Remaining rounds are played similarly; the game is won by the last surviving player(s).

Tring Central can also be played by any number. Each player writes a positive whole number on a slip of paper. The game is won by the player who wrote the lowest unduplicated number. (Tactical note: some numbers seem to be surprisingly successful in this game - 2 often sneaks in. A devastating tactic is to make a public announcement that you intend choosing 1!)

Meantime is another for any number of players. Each player writes a whole number from 1 to 100. The prize is won (or most likely shared) by the player(s) nominating the number closest to the mean of all the numbers chosen. Of course, this is a pretty simple-minded affair since there's little incentive for anyone to choose any number other than 50, but it makes a good introduction to the following game:

Econometricperson Each player (there can be any number) writes a whole number from 1 to 100. The prize is won by the player(s) nominating the number nearest to two-thirds of the mean of all numbers chosen. It's particularly interesting to play this for several rounds and see the way the winning number changes as the game goes on.

Finally, Middler, a game for just three persons, each of whom needs a set of ten cards, numbered from 0 to 9. There are ten rounds of play, and in each round each player simultaneously plays one card. Whoever played neither the highest, nor the lowest, but the intermediate card wins the round, and scores the total value of the three cards played. (If two players play the same value their cards are ignored, and the player of the third card wins the number of this card.) Further rounds are played in the same way - a card which has been played may not be used again. The overall winner is of course whoever has the intermediate of the three totals.

(Note: all these games have been played extensively in various postal versions. I'm particularly grateful to such people as David Watts, Robert Northcott and several others, including Douglas Hofstadter, who started me thinking about the whole world of Middler games - there are lots of versions of Middler, including two-digit variants, games for five players, etc, but this introductory version is quite demanding enough for beginners. Any teacher who'd like to know more about the whole fascinating world of playing games by post should get in touch with me at 6 Longfield Gardens, Tring, Herts HP23 4DN.) E

Mathematics in School, May 1994 13

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