Question 988759
Every {{{3*4=12}}} days Alice and Beatrix will both visit on the same day.
That will happen {{{30}}} times, on days 12, 24, 36, ....360,
because 12 goes 30 times into 365: {{{365/12=360/12+5/12=30+5/12}}} .


Every {{{3*5=15}}} days Alice and Claire will both visit on the same day.
That will happen {{{24}}} times, on days 15, 30, 45, ....360,
because 15 goes 24 times into 365: {{{365/15=360/15+5/12=24+1/3}}} .


Every {{{4*5=20}}} days Beatrix and Claire will both visit on the same day.
That will happen {{{18}}} times, on days 18, 36, 54, ....360,
because 20 goes 18 times into 365: {{{365/20=360/20+5/20=18+1/4}}} .


Every {{{3*4*5=60}}} days all three friends will visit on the same day.
That will happen {{{6}}} times, on days 60, 120, 180, ....360,
because 60 goes 6 times into 365: {{{365/60=360/60+5/60=6+1/12}}} .


If we count all the times that two friends visit at the same time {{{30+24+18}}} ,
we would be counting {{{3}}} times the {{{6}}} days that Alice, Beatrix and Claire will be visiting together,
so our count would be too high by {{{3*6=red(18)}}} .
So the number of days that exactly two friends visit Daphne is
{{{30+24+18-red(18)=30+24=highlight(54)}}}