After some matches were played, most of the information in the
table containing the results of the games was accidentally deleted.
What was the score in each match played?
Christmas trees are planted in a rectangular array of 10 rows and
12 columns. The farmer chooses the shortest tree in each of the
columns... the tallest tree from each of the rows ... Which is the
taller tree, A or B?
Three teams have each played two matches. The table gives the total
number points and goals scored for and against each team. Fill in
the table and find the scores in the three matches.
There were three Friday 13
ths in 1998,
this is the greatest number that can occur in any one year, and
there must be at least one each year.
Here is the solution from the Strabane Grammar
School Key Stage 3 Maths Club:
There are 14 possibilities to consider. These are detailed in
the table below together with the number of Friday 13 th
s appearing in each year:
Calendar calculations are very tedious if you have to do
everything by counting and it is quicker to use modulus
To use the fact that 31 days is 4 weeks and 3 days, we say 31 is
congruent to 3 modulo 7 and we write:-
31 3 (mod
31/7 = 4 remainder 3 or 31 3 (mod 7).
30/7 = 4 remainder 2 or 30 2 (mod 7).
29/7 = 4 remainder 1 or 29 1 (mod 7).
28/7 = 4 remainder 0 or 28 0 (mod 7).
Chin Siang explains the method as follows:
X can stand for any day (Monday, Tuesday, Wednesday, ...)
Looking at the table above, you will notice that X, X+1, X+2,
X+3, X+4, X+5 and X+6 all occur at least once and at most three
times. Thus, sometime in the year the thirteenth of the month will
be on each of the different days of the week at least once and at
most three times. For the thirteenth to be a Friday the first of
the month must be a Sunday. This can only occur three times in the
year, in February, March and November, when the 1st January is a