Number Grid

Friday 13th July 2007 Number Grid Coursework For this piece of coursework, I will investigate the difference when 2x2, 3x3, 4x4, 5x5 and rectangle snapshots are taken from a 10x10 number grid and have their corners multiplied and the difference worked out. For the first part, I will use 2x2 snapshots. 2x2 Boxes Box 1 2 3 2 3 2x13=26 --> 36-26=10 3x12=36 Box 2 32 33 42 43 32x43=1376 --> 1386-1376=10 33x42=1386 Box 3 6 7 6 7 6x17=102 --> 112-102=10 7x16=112 Box 4 5 6 5 6 5x16=80 --> 90-80=10 6x15=90 I have noticed the pattern here. Whenever the numbers are diagonally multiplied and then the difference is found, you always end up with 10. The hypothesis I am going to make is that if I was to work out the difference of another box taken from a 10x10 in a 2x2 snapshot, the difference I will find will be 10. Box 5 25 26 35 36 25x36=900 --> 910-900=10 26x35=910 My predictions that I made earlier about 'Box 5' have turned out to be correct as when I multiplied the numbers in the 2x2 box and worked out the difference, I was left with 10. I should now try the same method but with boxes of 3x3 dimensions. 3x3 Boxes Box 1 2 3 1 2 3 21 22 23 x23=23 --> 63-23=40 3x21=63 Box 2 33 34 35 43 44 45 53 54 55 33x55=1815 --> 1855-1815=40 35x53=1855 Box 3 4 5 6 24 25 26 34 35 36 4x36=504 --> 544-504=40 6x34=544 I

  • Word count: 1645
  • Level: GCSE
  • Subject: Maths
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Emma's Dilemma

Emma's Dilemma In this investigation, I will be attempting to find out the formula that would give me the number of possible arrangements for any group of letters, even if the group contains the same letters. To find this out, I will be investigating the possible arrangements for different groups of letters and from there I will be then using the number of arrangements for each of these groups to find a formula. I will start off with groups of different letters and find the formula for that. The first group of letters I will start off with is the group 'LUCY': . LUCY 2. LUYC 3. LCUY 4. LCYU 5. LYCU 6. LYUC 7. ULCY 8. ULYC 9. UYCL 0. UYLC 1. UCLY 2. UCYL 3. CLUY 4. CLYU 5. CYLU 6. CYUL 7. CULY 8. CUYL 9. YLCU 20. YLUC 21. YULC 22. YUC L 23. YCUL 24. YCLU Therefore for a group of four different letters there will be 24 different arrangements. I will now attempt to find out the number of arrangements for a group of 3 different letters, 'EMO': . EMO 2. EOM 3. MOE 4. MEO 5. OEM 6. OME So there are 6 possible different arrangements for any group of 3 different letters. I am now going to try to find out the number of arrangements for a group of 2 different letters, 'EM': . EM 2. ME Therefore, there are only two different arrangements for any two letter group of different letters. I also used this method to find out how many different

  • Word count: 1814
  • Level: GCSE
  • Subject: Maths
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