FA Carling PremiershipAuthor(s): Bernard MurphySource: Mathematics in School, Vol. 30, No. 2 (Mar., 2001), pp. 34-35Published by: The Mathematical AssociationStable URL: http://www.jstor.org/stable/30212153 .

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FA CARLING

PREMIERSHIP

by Bernard Murphy

(Last week's positions in brackets)

1. Manchester United (1)

2. Leeds United (2)

3. Liverpool (3)

4. Arsenal (4)

5. Chelsea (5)

6. Aston Villa (6)

7. Sunderland (7)

8. West Ham United (8)

9. Everton (10)

10. Tottenham Hotspur (9)

11. Newcastle United (12)

12. Middlesbrough (13)

13. Leicester City (11)

14. Coventry City (14)

15. Southampton (15)

16. Wimbledon (16)

17. Derby County (17)

18. Bradford City (18)

19. Sheffield Wednesday (19)

20. Watford (20)

HOME AWAY LAST 10 LU

MATCHES a- c O W D L F A W D L F A W-D-L

_.

31 70 +40 12 4 0 49 13 9 3 3 27 23 7-2-1 W4

31 60 +15 11 1 4 25 12 8 2 5 24 22 5-1-4 L3

31 59 +23 10 3 3 26 11 7 5 3 21 13 6-4-0 W3

31 57 +24 12 2 2 35 12 5 4 6 21 20 5-2-3 W3

31 55 +15 9 4 2 26 10 6 6 4 15 16 5-5-0 W1

32 49 + 9 7 6 2 19 8 6 4 7 17 19 5-4-1 W2

31 48 + 4 8 6 2 25 15 5 3 7 25 31 2-4-4 W2

31 45 - 5 9 4 2 25 21 3 5 8 17 26 5-1-4 L1

32 44 + 9 6 8 1 32 18 5 3 9 21 26 4-2-4 W1

31 43 + 9 8 2 5 32 20 4 5 7 15 18 2-3-5 L1

31 43 + 8 8 4 3 34 14 4 3 9 18 30 6-1-3 W1

31 43 - 7 8 3 5 17 19 4 4 7 18 23 4-3-3 W2

30 41 - 3 9 2 5 27 22 3 3 8 16 24 3-3-4 L1

32 38 - 2 10 1 6 32 20 0 7 8 8 22 3-0-7 L2

31 34 -17 6 4 5 20 17 3 3 10 17 37 4-2-4 L1

31 32 -17 6 6 4 27 22 1 5 9 15 37 1-2-7 L3

31 31 -10 5 2 9 19 23 3 5 7 17 23 3-3-4 W1

31 26 -27 4 7 4 17 23 2 1 13 11 32 2-2-6 L4

31 21 -31 4 3 8 16 18 1 3 12 11 40 2-2-6 L3

31 19 -37 4 3 8 19 25 1 1 14 9 40 1-2-7 L1

622 858 0 156 75 80 522 343 80 75 156 343 522 75-48-77 W20 (a) (b) (c) (d) (e) (f) (g) (h) (i) (j) (k) (1) (m) (n) DO

L20 (oh!)

34 Mathematics in School, March 2001 The MA web site www.m-a.org.uk

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Questions At any stage in the season can the total of the games played, column (a), be odd?

At the end of a season when each team has played 38 games, with three points for a win and one point to each team for a draw, what is the maximum possible points total (b)? What is the minimum?

Is it a coincidence that the goal difference column total (c) is 0?

Why do the totals appearing under 'Home', (d) to (h), mirror those under 'lway', (i) to (m)?

The total number of games won, (d)+(i), is 236. 'Total points' minus 'total played', (b)-(a), is also 236. Why is this always true?

Under 'Last 10 Matches' (n) why isn't 'total won' equal to 'total lost'?

Under 'current streak', (oh!) which shows recent winning, drawing or losing sequences, 'total wins' is the same as 'total losses'. Is this a coincidence? M

Reference Data from The Times, 8 April 2000.

Keywords: Games; Football.

Author

Bernard Murphy, Crompton House School, Rochdale Road, Shaw, Oldham OL2 7HS.

Solutions to Puzzles, Pastimes, Problems Produce Positive Pnumeracy Section 1

1.(a) Number chosen is 10+b-*80+b-*800+10b*- 802+ 10b-*8 +b+2 = 10+b.

(b) Number chosen is 10+b*60+b-*600+10b* 604+

10b-*-6+b +4= 10+b.

(c) Number chosen is 20+b-*80+b-*800+10b*

8+b-*8+b+12= 20+b.

2. a-2a*2a+3-10a+15-+10a+ll=10(a+1)+1.

3. a<10, 10b+c>10; +10b+c+a-50b+5c+5a-

50b+5c+6a-1OOb+ 10c+ 12a+100b + 10c+ 1la* 100b+ 10c + 1 la-1 = 10(10b +c +a)+(a-l).

4. a <b; - b-2+5b-10+5b-10+a+10b-20+2a- 10b-11 + 2a-, 10b-11 +a= 10(b-1)+(a-l).

Section 2

1. 12345679x9= 111111111 so (9xA)x12345679= Ax111111111 =AAAAAAAAA.

2.(a) 3x7x1lx13x17= 111111 so Ax3x7x1lx13x37= Ax111111=AAAAAA.

(b) 3x7x13x37= 10101 so ABx3x7x13x37=ABx10101 = ABABAB.

3. 7x11x13= 1001 so ABCx7xl 1x13= ABCx1001 =ABCABC.

Section 3

1.(a) Number chosen is 100x+10(7-x)+x=91x+70+ 13x+ 10-,x rem. 10.

(b) Number chosen is 100x+ 10(14-x)+x= 91x+ 140+ 13x + 20-,x rem. 7.

(c) Number chosen is 100x+10(13-x)+x=-91x+130+ 7x +10+x + 1 rem. 7.

2. Numbers chosen are a, b and c. Two-digit numbers are ab, ac, ba, bc, ca and cb which are equivalent to 1Oa+b, 1Oa+c, 10b+a, 10b+c, lOc+a and 10c+b, respectively. Sum of two-digit numbers is 22(a+b+c) and sum of original numbers is a+b+c. .'. Division gives 22.

3. 10a+b+O(a+6)+(b+2)= 100+10(a-4)+(b+2)-, 10(a-4)+(b + 2)+ 10(a-4)+(b + 3)

.'. 10a+b - [10(a-4)+(b+3)]= 1Oa+b-lOa+ 10x4-b-3 = 37.

Mathematics in School, March 2001 The MA web site www.m-a.org.uk 35

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