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The Christmas Puzzle The pictures in the grid each represent a number between 1 and 10. Using the totals of each row and column, can you work out what the value of each shape is?

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45 34 48 43 33 36 29 34 46 38 42 40 46 343050 Answer

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Now make up your own Christmas puzzle. Make sure that it can be solved.

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On the first day of Christmas my true love sent to me: A partridge in a pear tree. On the second day of Christmas my true love sent to me: Two turtle doves and a partridge in a pear tree. On the third day of Christmas my true love sent to me: Three French hens, two turtle doves and a partridge in a pear tree. Forth day....Four calling birds, 3 French hens, etc. Fifth day...Five gold rings, four calling birds, etc. Sixth day...Six geese a-laying, five gold rings, etc. Seventh day...Seven swans a-swimming, six geese a-laying, etc. Eight day...Eight maids a- milking, seven swans a-swimming. Ninth day...Nine drummers drumming, etc. Tenth day...Ten pipers piping, etc. Eleventh day...Eleven ladies dancing, etc. Twelfth day...Twelve lords a-leaping, etc. The Twelve Days of Christmas

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How many presents did ‘my true love send to me’ on: a)the third day? b)the fifth day? c)the tenth day? How many presents did ‘my true love send to me’ over the twelve days in total? What happens if there were 20 days of Christmas instead of twelve? How many presents would ‘my true love sent to me’ over the twenty days in total? Answer

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Christmas Tangrams The Tangram is a puzzle made from cutting a square into seven pieces in the following way. 8 cm

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How many of these shapes can you make? Which shape has the biggest area? Which shape has the longest perimeter? Answer

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Santa had just finished loading the 3691 125when 10 + 24 realised he couldn’t 67 5a single reindeer. “27689 2me” he said. “Where have they gone. If we don’t 60 ÷ 100soon we’ll never get round all the children tonight.” He grabbed 900 – 386 2396 + 5343and rang it loudly. He waited and listened, but nothing happened. “Come on boys”, he muttered, or 1191 3I’ll have to phone the 2 ÷ 100and 319 2 them to send some more deer. Just then there came a 8 47077 from behind the stables. Christmas Calcogram

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First Santa saw a pair of 23596 + 33738then two 1879 3then at last the whole of Rudolf appeared. “8.5074 ÷11Santa. Did you like our joke? Don’t look so worried. The others are all ready but they’re hiding in a 463 8in the 6 9619.”He smiled. “They know you’re the 9000 – 3492really.” “Alright, come on, let’s 12 ÷ 20” said Santa, with a 923 5 of relief. He got out 257 2list. “Now let’s see, I’ve got a computer for 28867 11 and the637 ÷ 1000 for Gemma, and the bike for 3 246017.” “1.0101 0.4”chuckled Santa and off they went. Answer

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The Christmas Star Here is a Christmas Star How many triangles can you find? Show where the triangles are as clearly as possible. You will need to draw more than 1 diagram Answer

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The Christmas Star Here is a more complicated Christmas Star How many triangles can you find? Show where the triangles are as clearly as possible. You will need to draw more than 1 diagram

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Packing The elves in one of Santa’s workshops always pack identically sized parcels (2 units by 1 unit) into trays which are 2 units wide but which have different lengths. How many different ways can the parcels be packed into a 3 by 2 tray?

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How many different ways can the parcels be packed into a 3 by 2 tray? 3 Ways How many different ways can the parcels be packed into a 4 by 2 tray? Investigate how many different ways the parcels can be packed into trays 2 units wide but with different lengths? Can you find a general rule? Answer

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How many arrangements are there for a 20 by 2 tray? Extension What happens if the tray is always 3 units wide? Answer

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Solve the algebraic clues to find the letters in the name of a Christmas character. You will need to put the letters in the correct order.

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Rules of algebra a + bmeans the value of a added to the value of b c – d means take away the value of d from the value of c 3xmeans 3 times the value of x 3x = 3 × x pqmeans p × q abcmeansa × b × c e / m meanse ÷ m h² meansh × h ( h squared)

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Name the Christmas Character abcdefghijklm 2468101214161820222426 nopqrstuvwxyz 28303234363840424446485052 Clue 1 = k - j Clue 2 = e + m Clue 3 = z / a Clue 4 = 5e k – j = 22 - 20 = 2 = a 10 + 26 = 36 = r z ÷ m = 52 ÷ 2 = 26 = m 5× e = 5 × 10 = 50 = y Unscrambling gives… Mary

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1)Clue 1 = 4eClue 2 = d – c Clue 3 = 7b Clue 4 = y – f Clue 5 = d + e – h 2)Clue 1 = 5bClue 2 = 2j + 2 Clue 3 = t / b Clue 4 = 3e + dClue 5 = 2j – 2 3)Clue 1 = bcClue 2 = cd – cClue 3 = p / a Clue 4 = e(a + 1)Clue 5 = c²Clue 6 = 2a² Clue 7 = 2b ² Now make up your own clues for famous Christmas Characters abcdefghijklm 2468101214161820222426 nopqrstuvwxyz 28303234363840424446485052 Answer

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Designing Snowflakes Use isometric (triangular dotty) paper Your designs must have 6 lines of symmetry Your designs must have rotational symmetry order 6 Grid

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© D Cavill 2004

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Answers

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= 1 = 3 = 2 = 4 = 5 = 10 = 9 = 8 = 7 = 6 Back

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The Twelve Days of Christmas On the third day, 6 presents were sent. On the fifth day, 15 presents were sent. On the tenth day, 55 presents were sent. Altogether, over the twelve days 1 + 3 + 6 + 10 + 15 + 21 + 28 + 36 + 45 + 55 + 66 + 78 = 364 presents Back

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Note that the number of presents given each day is a triangular number and the sum of the first n triangular numbers is called a tetrahedron number. Hence 364 is a tetrahedron number. Over 20 days the total number of presents would be: 364 + 91 + 105 + 120 + 136 + 153 + 171 + 190 + 210 = 1540. A general formula to give the number of presents on day n (triangular numbers) ½ n (n +1) A general formula to give the number of presents sent altogether over the first n days is: 1 / 6 n³ + ½ n² + 1 / 3 n = 1 / 6 n (n + 1)(n + 2) Back

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Tangram Answers Back

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Santa had just finished loading the SLEIGH when HE realised he couldn’t SEE a single reindeer. “BLESS me” he said. “Where have they gone. If we don’t GO soon we’ll never get round all the children tonight.” He grabbed HIS BELL and rang it loudly. He waited and listened, but nothing happened. “Come on boys”, he muttured, or ELSE I’ll have to phone the ZOO and BEG them to send some more deer. Just then there came a GIGGLE from behind the stables. First Santa saw a pair of HEELS then two LEGS then at last the whole of Rudolf appeared. “HELLO Santa. Did you like our joke? Don’t look so worried. The others are all ready but they’re hiding in a HOLE in the HILLS”He smiled. “They know you’re the BOSS, really.” “Alright, come on, let’s GO ” said Santa, with a SIGH of relief. He got out HIS list. “Now let’s see, I’ve got a computer for LESLIE and the LEGO for Gemma, and the bike for ISOBEL.” “HOHOHO”chuckled Santa and off they went. Christmas Calcogram Back

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5 5 5 10 35 Triangles Altogether Back

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Size of trayNumber of Arrangements of Parcels 1 by 2 2 by 2 3 by 2 4 by 2 5 by 2 6 by 2 7 by 2 8 by 2 1 2 3 5 8 13 21 34 Back

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To find out how many ways there are to pact a 7 by 2 tray, add together the number of ways to pack a 5 by 2 tray and a 6 by 2 tray To find out how many ways there are to pact a n by 2 tray, add together the number of ways to pack a n-1 by 2 tray and a n-2 by 2 tray W n = W n-1 +W n-2 Ways to pack a n by 2 tray Back

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1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765 There are 10946 Ways to pack a 20 by 2 tray! This number sequence is called the Fibonacci Sequence after one of the greatest European mathematicians of the middle ages, Leonardo of Pisa, better known as Fibonacci. Back

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Name the Christmas Character 1)Santa 2)Jesus 3)Rudolph Back

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© D Cavill 2004

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