Curiouser and CuriouserAuthor(s): Helen MorrisSource: Mathematics in School, Vol. 28, No. 2 (Mar., 1999), pp. 44-45Published by: The Mathematical AssociationStable URL: http://www.jstor.org/stable/30211986 .

Accessed: 06/04/2014 16:46

Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at .http://www.jstor.org/page/info/about/policies/terms.jsp

.JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range ofcontent in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new formsof scholarship. For more information about JSTOR, please contact support@jstor.org.

.

The Mathematical Association is collaborating with JSTOR to digitize, preserve and extend access toMathematics in School.

http://www.jstor.org

This content downloaded from 100.2.40.176 on Sun, 6 Apr 2014 16:46:47 PMAll use subject to JSTOR Terms and Conditions

uriouser andurouser

cun-ouser

Compiled by Helen Morris

Puzzle Corner

1. What is 2 + 11 - 1? 12, obviously! How? 2. A/,, Bc+ D/EF + GHI is the sum of three fractions.

Make the total 1 by giving the letters A - I the values 1 - 9.

3. Set down the figures 1, 2, 3, ..., 9 so that together only with + signs the expression has the value 100. No other mathematical signs may be used.

Contributed by lan F Smith, Sanderstead, Surrey

Squares are Odd A conjecture; is it valid? The square of every odd number is the sum of three squares. 32 = 9 = 12 + 22 + 22 52 = 25 = 02 + 32 + 2 72 = 49 = 22 + 32 + 62 92= 81 = 12 + 42 + 82 112 = 121 = 22 + 62 + 92 132 = 169 = 02 + 52 + 122= 32 + 42 + 122 152 = 225 = 52 + 102 + 102 = 22 + 52 + 142

= 02 + 92 + 122 172 = 289 = 12 + 122 + 122 = 02 + 82 + 152

Another conjecture; is it valid? Three times the square of every odd number is the sum of three squares.

3 x 52 = 27 = 12 + 12 + 52 3 x 52 = 75 = 12 + 52 + 72 3 x 72 = 147 = 12 + 52 + 112 3 x 92 = 243 = 12 + 112 + 112 = 32 + 32 + 152

= 52 + 72 + 132

Contributed by D B Eperson, Worthing, Sussex

Squaring the E

Cut the E into 7 parts with 4 straight cuts. The parts can be reassembled to make a square.

Guess Who's Coming to Dinner The Mayor of London is organizing a dinner party, a very small dinner party. He will be asking his father's brother-in-law, his brother's father-in-law, his father-in-law's brother, and his brother-in-law's father. How many dinner guests will there be if the party is to be as small as possible?

Adapted from 'Rediscovered Lewis Carroll Puzzles', Edward Wakeling, 1995

Down Our Street

Looking out of my window I can see five houses, all with odd numbers. Looking right, further down, at the end of our street, is house number 1. The middle house of the five that I can see is a prime number, but the other four are not prime numbers. What is the number of the widest house?

One, Two, Three, Four, Five... Once I Caught a Fish Alive

Accompanying this well-known nursery rhyme is a finger counting sequence to assist in toddlers' learning of their numbers 1 -- 10. The sequence starts on the little finger of the right hand up to the thumb of the right hand (1->5), then moves on to the left hand for 6 -> 10, this time starting with the thumb and moving along to the little finger. The fingers open out from the fist as the number is revealed.

44 Mathematics in School, March 1999

This content downloaded from 100.2.40.176 on Sun, 6 Apr 2014 16:46:47 PMAll use subject to JSTOR Terms and Conditions

one. two, three. OnreOcaugt.. Six. seveight Then leNthimgo... four, fiVe nine. ten

whly..? Becouse he bit ... This little finger...

This is not a system that I naturally would have chosen to count from 1 to 10. I recently asked a group of 11 ITT students in Lancaster to count from 1 -- 10 using their fingers and 11 different methods were demonstrated.

And yet, the method chosen could be crucial to your survival. There is a story that a Japanese girl was trying to pass herself off as being Chinese during the 1939-1945 war. She was doing very well until she was seen counting to 10 with her fingers, and was then revealed as being the Japanese enemy. She started counting with an open hand, putting fingers down as they were named, apparently a Japanese system-she should have started with a closed hand to be like the Chinese!

In Lancaster we discovered that there was no accepted system and yet members of tribes in Africa have been able to be identified by their finger counting methods.

A method developed by the Venerable Bede, in the 8th century, gave a complicated hand system for all numbers up to 1,000,000. The first nine numbers using the left hand, with some not inconsiderable personal difficulty, are: 1. Little finger down, bent at middle knuckle 2. and the ring finger down 3. and the middle finger down 4. and raise the little finger 5. and raise the ring finger 6. and raise the middle finger, bend down ring

finger 7. and raise the ring finger, bend down middle

finger at bottom joint 8. and the ring finger 9. and the middle finger. From Tanzania:

1. Raise right index finger 2. Raise and spread out right index and middle

fingers 3. Raise and spread out right middle, ring and

little fingers 4. Raise four right fingers with a gap between

the middle and ring fingers 5. Raise right clenched fist 6. Raise and spread out middle, ring and little

fingers of each hand 7. 4 on right and 3 on left 8. 4 on right and 4 on left 9. 5 on right and 4 on left

10. Right and left clenched fists

Some number words relate to the ways of representing them physically. Zulu:

1. Nyi meaning being alone (little finger)

2. Bili raise a separate finger 3. Tatu raise another separate

finger 4. Ne to pick up 5. Hlanu ? 6. Tatisitupa take the right thumb 7. Ikombile point with forefinger

of right hand 8. Shiya'ngalambile leave out two fingers 9. Shiya'ngalalonye leave out one finger

10. Shumi make all fingers stand The Oksapmin tribe of Papua New Guinea are more adventurous, pointing at various parts of the body representing different numbers.

,3 r(7,3

e-1 Iza I 26

20

Solutions Puzzle Corner 1. 2 = TWO; add 11 = TWOELEVEN; subtract 1 =

TWOELEVEN = TWELVE 2. /34

+ ~,68

+

124 3. 1 + 3 + 6 + 7 + 8 + 59 + 2 is one of many solutions.

Squaring the E

Guess Who's Coming to Dinner There is only one guest.

Down Our Street The widest house is numbered 51.

Contributions to this column are most welcome and should be sent to: Helen Morris, 57 Woodplumpton Lane, Broughton, Preston PR3 5JJ.

Mathematics in School, March 1999 45

This content downloaded from 100.2.40.176 on Sun, 6 Apr 2014 16:46:47 PMAll use subject to JSTOR Terms and Conditions