Sharing Trophies

Saturday 1st March 2025

Addel Adgood, a hard-working student, has earned a number of trophies in the last month. She wants to share them among her three younger brothers, according to these fractions of the total:

• The eldest brother receives half of them
• The middle brother one-third of them
• The youngest brother one-eighth of them

At first glance, it seems impossible to divide the number of trophies she has exactly into halves, thirds, and eighths. Then, someone suggests 'borrowing' one extra trophy from a friend, temporarily increasing the number of trophies Addel has. Now the given fractions are possible and there will be one trophy left over, which can be returned to the friend.

How many trophies did Addel initially have?