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Writ Large

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?

Mathland Election

Age 11 to 14
Challenge Level


On Mathland TV a political commentator summed up an election result as follows.


A Labour majority of $1729$ last time has been turned into a Conservative majority of $1654$ in this election and the conservative candidate has obtained $38\%$ of the poll. Labour has taken second place. The Liberal Democrat has obtained only $14\%$ of the poll and has been beaten into fourth place by the SNP candidate who has $50$ more votes than the Liberal Democrat.

Given that there were just four candidates and that the figures quoted were exact find the number of votes polled for each candidate.


[This question comes from the book 'Mathematical Challenges' published in 1989 for the Scottish Mathematical Council by Blackie, ISBN 0216 92622X]