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PostPosted: Tue Jan 16, 2007 11:33 pm 
hi there is there anyone who could be our saviour. my son got the following question in his maths homework today;
look at this magic square nubers arsmade by multiplying instead of adding.
sorry can't draw boxes
1st box: 36 16 3
these are
the nos 36 16 3
given to us 1 12 144
48 9 4
we have to solve these poblems; a)what are the properties of the product magic square?(HINT: the number in the middile is important).
b)will the product magic square work if the rule is not followed?
c)copy and complete these magic square.

square A) ? ? 2
1 14 196
98 ? ?


square B) ? ? 4
1 8 ?
16 ? 2


thanx for your help in advance. iknow it is too alte but hope to get some response as he would be expecting answers from me in the morning. :cry:


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PostPosted: Wed Jan 17, 2007 8:39 am 
Hi not sure exactly what they want.
the two squares to solve are easy as they give you enough that you just have to basically fill in the missing squares.. ie they give you a complete diagonal or row so you know the total, so then just divide that by a row only missing one number etc....

the other bit... the only rule I can see is that the middle number is the square root of the largest number, and in all the rows or diagonals the middle number is effectivly the middle number in a sequence.. i,e 3,12,49..is just multiplying each number by 4 etc.... but I'm sure there;s a more correct answer which someone will come along with..

steve


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PostPosted: Wed Jan 17, 2007 8:58 am 
My first thoughts on this question.


The numbers either side of the 12 in the centre when considered vertically, horizontally or diagonally are in a consistent ratio.

So ratio of 36:12=12:4 (=3:1)
16:12=12:9(= 4:3 = 1.333:1 approx)
48:12= 12:3 (=4:1)
144:12=12:1 (=12:1)

These ratios are based on the factors of 12=3x4

Square A is
28, 49, 2
1, 14, 196
98, 4, 7

using factors of 14 =2x7

Square B is
32, 4, 4
1, 8, 64
16, 16, 2

Using factors of 8=4x2 (not 2x4 see note below)

A point to note is that the top left to bottom right factor in the first 2 magic squares is less than the bottom left to top right factor.

This gives us a number in the middle top box which is greater than the central number.

In the third magic square, the top left to bottom right factor is greater than the bottom left to top right factor.

So the number in the top middle box will be less than the central square.


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