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IMSO 2007 Mathematics - International Exploration Question 5

IMSO Maths · IMSO 2007 Mathematics - International Exploration

Question 5

The rectangular array below must be crossed from the top row to the bottom row.
(i) Only up, down, left and right moves are allowed; no diagonal moves.
(ii) A route visits every cell at most once, although different routes may share cells.
(iii) The digits on a route form at least two repeated blocks. Examples: 1,2,1,2,1,2 has block 1,2; 2,1,3,2,1,3 has block 2,1,3; 1,3,4,2,1,3,4,2 has block 1,3,4,2. The final block need not be complete.

Question illustration

Draw as many routes as you can from any top-row cell to any bottom-row cell that obey these rules. The red route above is already printed in the source.