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You might like to look at Counting on Letters before you try this problem.

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 this array?

E U R O M
U R O M A
R O M A T
O M A T H
M A T H S

Thank you to Henriett Keri from Miskolc in Hungary for bringing this task for discussion at our EuroMaths conference, with Josephine Burgess from Bedfordshire in England, and Inga Bendtsen and Karina Leth Hansen from Aarhus in Denmark. The task was contributed by Eva Pinter Kovacsne from Tiszaujvaros, Hungary.