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Move a Match

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

Congratulations to everyone who helped crack this Toughnut, and correctly spotted, as Samantha has said:
"In order for this solution to be possible, the number of matches in each of the four groups must be consecutive."

So aj explained for 10 matches:
"for 10 matches, you can arrange them as 4,3,2,1. Take a match from each pile from the left and add them to the pile at the end. You end up with 3,2,1,4."

Congratulations to everyone who noticed that in general you take from all but the smallest pile, and place the matches on the smallest pile, as Jake and Hannah (St Peter's School,Wrecclesham):