# Sunday Times Teaser 3193 – Balanced Education

### by Danny Roth

#### Published Friday December 01 2023 (link)

George and Martha are headmaster and secretary of Millimix School. There are 1000 pupils divided into 37 classes of at least 27 pupils each; each class has at least 13 members of each sex. Thus with 27 x 37 = 999, one class has an extra pupil. The classes are numbered 1-37.

Martha noted that, taking the class with the extra pupil, and adding its class number to the number of girls in that class and a power of two, she would arrive at the square of the class number. Furthermore, the class number equalled the number of classes in which the girls outnumbered the boys.

How many boys are in the school?

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More complex (wanted to do something slightly different).