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Exploring Wild & Wonderful Number Patterns

EWWNP means Exploring Wild and Wonderful Number Patterns Created by Yourself! Investigate what happens if we create number patterns using some simple rules.

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Worms

Place this "worm" on the 100 square and find the total of the four squares it covers. Keeping its head in the same place, what other totals can you make?

Sept03 Sept03 Sept03

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

This problem was very accessible and all the solutions received were neat and concise and similar to the one below.

Congratulations to Ashley of Bentley Park College, Sana, Jenny, Chris and Rosion of Madras College, St. Andrews, as well as
Mary of Birchwood High School, Andrei of School 205 Bucharest, Chen of the Chineses High School, Singapore.

In this 903-digit number, the first 900 digits comprise 1, 2, 3, 4, 5 as a sequence of recurring digits with the last three digits being being 1,2 and 3.

Thus, the sum of all the digits = (900/5) x (1+2+3+4+5)+1+2+3 = 180x15+6 = 2706