From a group of any 4 students in a class of 30, each has exchanged
Christmas cards with the other three. Show that some students have
exchanged cards with all the other students in the class. How many
such students are there?
Suppose you had to begin the never ending task of writing out the
natural numbers: 1, 2, 3, 4, 5.... and so on. What would be the
1000th digit you would write down.
How many ways can you write the word EUROMATHS by starting at the
top left hand corner and taking the next letter by stepping one
step down or one step to the right in a 5x5 array?
We have received correct solutions from Sarah
Dunn, Ben Falconer, Fern Smith and Ian Downie, all from Madras
College. Well done to you all.
They all used a similar argument:
Since all the votes add up to 100%
$38\% + 38\% -1654 +14\% + 50 + 14\% = 100\%$
$104\% - 1604 = 100%$
therefore $4\% = 1604$ votes
$1\% = 401$ votes
and $100\% = 40100$ total votes.