Teaser 3205

Colum’s Columns of Bob’s Bobs

Colum played with Grandpa Bob’s collection of shilling coins. He used them to make minted-year columns for all years from 1900 to 1940 inclusive (in order, in line and touching). Exactly twelve columns had just one coin. This arrangement resembled a bar chart. Pleasingly, it was symmetric about the 1920 column (the tallest of all) and each column’s coin tally was a factor of its year. The total tally was a prime number.

Later, Bob found eight more shilling coins in an old tin. Colum found that these added one to each of eight columns. Curiously, everything stated above about the arrangement still applied. If I told you the year and final tally for one of those eight columns you could be sure of the total final tally.