# Same Maths Coursework

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Ex 1.2: Results for 2004 Months ( n ) Start day 1 Thursday 2 Sunday 3 Monday 4 Thursday 5 Saturday 6 Tuesday 7 Thursday 8 Sunday 9 Wednesday 10 Friday 11 Monday 12 Wednesday Therefore, we can see that the dates are thus: 1, 4, 7 = same 2, 8 = same 3, 11 = same 5 6 9, 12 = same 10 As you can see, the dates which fall on the same day are not the same as in the study sample Ex 1.1, so there is no pattern here.Ex 4.6 Starting July 4th n date 1 4 2 12 3 20 4 28 The above table gives a formula of 8n – 4.I have noticed that descending diagonally left is always n = 6n – x, where x depends on which date you choose to start with. Columns) is always n = 7n – x; and that descending diagonally right gives n = 8n – x. Studying relationships between adjacent numbers I drew a box around 4 numbers: Ex 5.1 Starting 2nd August 2 3 2 x 10 = 20 9 10 3 x 9 = 27 The difference is 7.Ex 3.2 The second row in June: n 1 6 3 7 4 8 5 9 6 11 7 12 As you can see from the table above, the formula is quite simple: n = n 5 Ex 3.3 The third row in June: n 1 13 2 14 3 15 4 16 5 17 6 18 7 19 The above table gives another formula: n = n 12 Ex 3.4, Finally the fourth row in June: n 1 20 2 21 3 22 4 23 5 24 6 25 7 26 The final formula is n = n 19 Ex 3.5: These are the formulae for the rows in the month of June: First row: n = n Second row: n = n 5 Third row: n = n 12 Fourth row: n = n 19 I didn’t draw the table for 5th, but predict it as: Fifth row: n = n 26 The general expression is n = n x depending on the start date. Studying diagonal relationships Ex 4.1 Diagonally descending to the left, starting with 2nd January.n date 1 2 2 8 3 14 4 20 5 26 The difference is always 6.n date 1 9 2 15 3 21 4 27 The above table gives the formula n = 6n 3 Ex 4.3: Diagonally descending to the left, starting with 5th June.n date 1 5 2 11 3 17 4 23 5 29 This table gives the formula n = 6n – 1 Now I will study Diagonals descending to the right, to examine whether there is any similar relationship between these numbers. Ex 4.4 Diagonally descending to the right, starting with 3rd February.Ex 1.4 Results for 2001 Months ( n ) Start day 1 Monday 2 Thursday 3 Thursday 4 Sunday 5 Tuesday 6 Friday 7 Sunday 8 Wednesday 9 Saturday 10 Monday 11 Thursday 12 Saturday The matching months are: 1, 10 = same 2, 3, 11 = same 4, 7 = same 5 7 8 9, 12 = same As you can see, once again the results for the months that start on the same day show the same pattern as in Ex1.1 and Ex1.3.This clearly shows that there is indeed a pattern between the start days of the months each non – leap year.This formula makes sense because when you descend diagonally to the left, you travel foreword in time by one week minus a day, i.e. I found that this applies to any box of 4 numbers on the calendar.Ex 5.2 Starting 6th October 6 7 6 x 14 = 84 13 14 7 x 13 = 91 The difference is 7 again, as in Ex 5.1.