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BANQUET AT THE CASTLE

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There was a great banquet at the castle. Many kings and queens, princes and princesses, dukes and duccesses, knights and even bishops were expected.

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To know how much food is needed, the cooks should know the number of guests. They only knew that: if the guests were put by twos, threes, fours, fives, sixes and even sevens in the rooms, there always remained one guest alone in a room. How many guests were there?

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After helping the poor cooks, help the last guest to find his way to the banquet. The problem wouldn’t be the same without him!

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CROATIAN SOLUTION: 421 guests

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Romanian answer - from Lugoj

The least common multiple of 2, 3, 4, 5, 6 and 7 is 420, so, adding that last guest, who will, finally, find his way to the castle, we get 421 guests at the banquet. This is the smallest number of guests that solves the problem. However, there are other numbers that comply:

420 x 2 + 1 = 841

420 x 3 + 1 = 1261

420 x 4 + 1 = 1681... and so on

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Here we set the trail for the last guest to arrive to the banquet. We hope they will have fun!