CROSSNUMBER PUZZLES - amtt.com.au

1 DAVID I CLARKCROSSNUMBER PUZZLES FOR SECONDARY MATHEMATICS STUDENTSP ublished byAustralian Mathematics TrustUniversity of Canberra Locked Bag 1 Canberra GPO ACT 2601 AUSTRALIAC opyright 2012 AMT PublishingTelephone: +61 2 6201 Limited ACN 083 950 341 CROSSNUMBER PUZZLES for Secondary Mathematics Students ISBN with simple with a from Middle challenging with secondary Maths Day ..96iIntroductionCrossnumber PuzzlesCrossnumber PUZZLES are similar to their more familiar cousins, crossword PUZZLES , in that they con-sist of interlocked grids of across and down answers , each of which is the answer to a specific answers are, of course, numbers rather than words.

2 Unlike crossword PUZZLES the clues typicallyinvolve more than one answer, and answers often appear in more than one clue. It is rare that theanswer to a clue can be determined in difference from crossword PUZZLES is that CROSSNUMBER PUZZLES are solved a digit at a timerather than a whole answer at a time. A digit is teased out of one clue, and this in turn helps in findinga digit in another PUZZLES are something akin to detective stories. Clues are given, but the implications ofthe clue needs to be worked out before it is applied in furthering the solution of the puzzle.

3 Crossnum-ber PUZZLES are brain-teasers, and you can anticipate many hours of pleasant occupation in solvingthe PUZZLES in this book. The more challenging PUZZLES may take an hour or more, but the puzzlesthemselves and the solvers experience are so varied that it is not easy to suggest a par time. The onlypuzzles constructed with a particular solution time in mind are the Canberra Maths Day PUZZLES (seebelow).A unique feature of this book is that each puzzle comes with a solution guide which gives one possibleorder for solving the puzzle.

4 If you are stuck, the solution guide will tell you which cell or cells totackle next, without telling you how to do it. You can then still have the fun and satisfaction of solvingthe puzzle. If you are really stuck, you can look up the solution. But again, the solution guide willtell you which cells to look up so that you can continue solving the rest of the of the clues in the PUZZLES in this book have operations that go beyond simple arithmeticoperations of addition, subtraction, multiplication, division and averaging, but they are still accessibleto solvers who are unfamiliar with them.

5 There is a glossary of mathematical terms used in the is also a fully worked solution to a simple puzzle and some useful hints about solving cross-number PUZZLES , particularly starting PUZZLES are organized into six sections as described 1. These PUZZLES mainly use standard arithmetic operations addition, subtraction, multi-plication, division and 2. These PUZZLES are a bit different. The contexts are different, and therefore solution tech-niques have to be adapted. There tends to be a bit more logic in 3.

6 Each of these PUZZLES has a small story associated with it. You are asked to solve a problemakin to a logic problem, but using a CROSSNUMBER 4. These problems are rather harder than the others. You will generally need to use morethan one clue to make 5. These problems have more mathematics in them. They incorporate most of the conceptsin secondary maths, including algebra, trigonometry, differentiation and integration, summation andpowers and logarithms. Students will need a thorough understanding of these topics to solve 6.

7 These problems were devised for the Canberra Maths Day, where schools send a teamof five final-year college students to compete against other teams from other schools in a fun andchallenging day. The CROSSNUMBER contest is one of four events on the day. An interesting featureof the event is that each team is split into two halves, one half receiving the across clues, the otherreceiving the down clues. When one half of the team deduces the digit in a particular cell they tellthe supervisor who tells them whether they were correct and lets the other half of the team each half of the team relies on the other half to make progress.

8 Typically just a few of the teamsfinish in the allotted 45 minutes, with most of the others fairly book grew out of the PUZZLES I constructed for the Canberra Maths Day, and includes some ofthem. The maths day has run annually since the middle 1980s when it started life as the University ofCanberra Maths Day. It was given generous administrative and financial support from the AustralianMathematics are due to John Matthews, Ian Lisle, Tracy Huang, Vance Brown and Malcolm Brooks fortheir checking of PUZZLES in the book, and to Malcolm Brooks for helping to work out how thecrossnumber contest could be made to work as part of the maths book was typeset in TEX, the mathematical typesetting system designed by Donald Knuth.

9 Manycontributors have given freely of their time and expertise to extend the capabilities of TEX. The TikZ/ PGF package written by Till Tantau was used in the diagrams in this book. Finally, special thanksare due to Ian Lisle for expert advice on all things s CommentsThis book has been a labour of love. I have enjoyed constructing the PUZZLES , and coming backand solving them some months or even years later. I hope that it will be a fun and challenging forthose who enjoy mathematics. I also hope that using mathematics in a different context will enhanceunderstanding and occasionally lead to further explorations I am a firm believer in indirect ClarkUniversity of CanberraFebruary, fifth of13d3see16a,2d6 One less than a square7A multiple of4d8see3d,14d10see14d13A multiple of 71512d 17asee also17a,11d16 Three times3asee also2d1715a+ 5see also15a15d+ 13d23a+ 16a3A permutation of8a4see7a5see1d9 The square of13d1115a+ 12d12see15a,11d13see1a,1d,9d14A divisor(10a 8a)

10 1 Puzzle this puzzle each of the letters stands for a different 14a3see4d6 Half of11a8A multiple of13a911a 7d11A squaresee6a,9a13see8a14see1a,10d16see10d 17A multiple of13d1A power of 2213d= 11dmod2d43a+ 5d5see4d7see9a1016a 14a11see2d12see1a13see17a,2d,15d1513d 52 Puzzle Middle Earth Treasure HuntThe Middle Earth treasure hunt was contested by a team of hobbits and a team of elves. The hobbitswere Bilbo, Frodo, Merry, Pippin and Sam, while the elves team consisted of Celeborn, Galadriel,Arwen, Legolas and Gimli, the elf friend.