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Brothers & sisters

Joan has the same number of sisters as she has brothers, but her brother Alex has twice as many sisters as he has brothers.  If their family has fewer than 10 children how many of them are boys and how many are girls?

 

Answer: 4 girls and 3 boys.  Joan has the same number of sisters as brothers, we need to test only the combinations in which Joan has the same numbers of sisters and brothers up to 4 each.  If Joan has 5 sisters and 5 brothers, the family has 10 children  Once Joan's siblings are determined, we know that Matt has one more sister than Joan and one less brother.  We need to check only that the number  of Matt's sisters is twice that of his bothers.  

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The Opposite Hands

When the hour hand on a clock is between 12:00 and 1:00, during which 1-minute time interval are the minute hand and the hour hand pointed in exactly opposite directions?

 

Answer: ...between 12:32 and 12:33.  To be opposite the hour hand must be between 6 &7.  The hour hand moves five 1-minute marks during the same time that the minute hand sixty 1 minute marks.  When the hour hand is on the first minute mark, the time is about 12:12.  At the 2-minute mark, the time is about 12: 24, and at the 3-minute mark, the time is about 12:36.  At some point between the 2 & 3 minute mark, the minute and hours hands are opposite each other.  

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