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The St. Patrick's Day parade

The St. Patrick's Day parade

Recently, during the San Patricio parade, an interesting and curious riddle developed. The Grand Marshal gave the usual news in which he said: “The members of the Honorable and Old Order of the Hiberns will parade in the afternoon if it rains in the morning, but they will do it in the morning if it rains in the afternoon”. This gave rise to the popular saying that one should keep in mind that it will rain safely on St. Patrick's Day.

Casey boasted that he had paraded for a quarter of a century at the military stop on St. Patrick's Day, since he was a boy. I will ignore the curious interpretations that can be made from this comment and say that as age and pneumonia finally surpassed Casey, he left along with the immortal procession.

When the boys met again to honor St. Patrick on March 17 they discovered that there was a vacancy so embarrassing in their ranks that it ruined the parade and turned it into a funeral procession invaded by panic. The boys, according to custom, settled in rows of ten and marched a couple of blocks in that order with only nine men in the last row where Casey used to march because of a problem in his left foot. The band's music was so completely drowned out by the shouts of the spectators that they asked “what had happened to the type of lameness” that it was thought that it would be better to reorganize the formation on the basis of nine men per row since with eleven no it could.

But once again Casey was missed and the procession stopped when it was discovered that there were only eight men in the last row. There was a hurried attempt to form each row with eight men, then with seven, then with five, four, three and even two, but it was discovered that in each of these formations there was always a vacant space for Casey in the last row.

Then, even if it seems like a superstition, in all the rows it began to whisper that every time they started to march you could hear “the dragged foot” of Casey's passage. The boys were so convinced that Casey's ghost marched with them that no one dared to close the march.

The Grand Marshal, however, was a quick and intelligent guy who quickly left out the ghost ordering the men to march in an Indian line, so if Casey's spirit was there, he would be the last of the long procession in honor of the patron saint. .

Assuming the number of men in the parade did not exceed 7,000, Can you determine how many men marched in that parade?

Solution

When Casey was alive, the number of men was a multiple of 2, 3, 4, 5, 6, 7, 8, 9 and 10.

We take the least common multiple: 2,520, then subtract 1 to get the number of members without Casey. This could be the answer if it weren't for the phrase "with eleven you couldn't". Since 2,519 is divisible by 11 we have to take the next common multiple, 5,040, and then subtract 1 to get 5,039. As this number is not divisible by 11, and as higher multiples they would give answers above 7,000, we conclude that 5,039 is the correct answer.