The Ringing Bells

The small village of Bloemenfontein had two churches which were located quite near each other. The bells of the churches rang with different periods, the Church of the Five Trinities ringing every 5/3 seconds, the Church of the Eleven Pentalphan Saints every 11/5 seconds.

To summon the members of the congregations for service on Sundays, both churches would sound their bells for 12 minutes precisely at 11 am in the morning.

A peculiar effect with these bells was that every now and then people could only hear one bell ringing, which would confuse members of the congregations, resulting in an equal proportion going to the wrong church.

But this did not matter much, as the preachers of the churches actually were twins and would switch roles every other week or so, thus saving time in writing sermons to give more free time for their hobby of fishing.

The local bicycle shop owner Joop Visser, who was also the mayor of Bloemenfontein, had worked out that when the clappers of the bells struck within an interval of 0.6 seconds of each other, only one bell ring could be heard.

Visser, being a meticulous person, had also counted the number of bell rings with the aid of a sound recorder.

Being a business man, mayor Visser decided to hang up a poster on the large, spreading oak tree in the main plaza of the village.

The poster stated that the first person who could correctly say how many bell rings in total were heard during a period of 12 minutes each Sunday would win a new, red bicycle.

Entry fee for submitting an answer to Visser was ten guilders.

Visser received numerous payments and responses very quickly, but the first correct one was from a young computer nerd.

Under these conditions, what would you say is the number of rings heard from these bells sounding on Sunday mornings?

On the average how many congregation members do you figure would wind up at the wrong church on a Sunday?

 

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