A Roman General is inspecting his troops. The troops arrive in eight squares each headed by a Junior Officer, who marches in front of the square. After the inspection the General insists on a more democratic arrangement, and all the troops, the Junior Officers and the General form one large square and march off the parade ground.
Each of the eight squares of troops is the same size and is a complete square with no gaps. And the square that marches off, including the extra nine men, is also a complete square with no gaps.
What is the smallest number of troops that could do this?
And as this is a rather small number of troops for a General to command, what is the next smallest number?
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Answer at 9.00 on Monday