In Kakuro (also known as Cross Sums), no digits can be repeated in each sum. For example, 16 for two boxes must be 9 and 7 (or 7 and 9) and cannot be 8 and 8.
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October 2019 Brain Puzzler Solution
Q: How many factors of 155^9 are perfect squares and/or perfect cubes?
A: 37 factors of 155^9 are perfect squares and/or perfect cubes.
155 is a composite number composed of 5 x 31.
Therefore
155^9 = 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 31 x 31 x 31 x 31 x 31 x 31 x 31 x 31 x 31
25 Perfect Squares:
1: 1 is both a perfect square and a perfect cube.
4: Perfect squares with just 5s = 5^2, 5^4, 5^6, 5^8
4: Perfect squares with just 31s = 31^2, 31^4, 31^6, 31^8
Combining the 5s and the 31s Perfect Squares
4: 5^2 x 31^ 2, 5^4 x 31^2, 5^6 x 31^2, 5^8 x 31^2
4: 5^2 x 31^ 4, 5^4 x 31^4, 5^6 x 31^4, 5^8 x 31^4
4: 5^2 x 31^ 6, 5^4 x 31^6, 5^6 x 31^6, 5^8 x 31^6
4: 5^2 x 31^8, 5^4 x 31^8, 5^6 x 31^8, 5^8 x 31^8
12 Perfect Cubes:
Perfect cubes with just 5s = 5^3, 5^6 (already counted above), 5^9 (2)
Perfect cubes with just 31s = 31^3, 31^6 (already counted above), 31^9 (2)
Combining the 5s Perfect Cubes and the 31s Perfect Cubes
5^3 x 31^3, 5^6 x 31^3, 5^9 x 31^3 (3)
5^3 x 31^6, 5^9 x 31^6 (2)
5^3 x 31^9, 5^6 x 31^9, 5^9 x 31^9 (3)
Kahoot Student Survey: Which is better? A positive or negative slope?
Kahoot is amazing for compare/contrast and for taking the temperature of the class. The anonymity helps students express their thoughts without judgment.
Those who voted “negative” explained that it would be beneficial to lower money owed or cholesterol levels. The “positive” folks shared their examples of money saved or growth chart of a child.
But without knowing the application, one cannot tell if a positive or negative slope would be better. In hindsight, this would have been good to revisit right before the midterm exam! Kahoot link (this is the first of 7 questions).
September 2019 Brain Puzzler Solution
Q: If 6 people take 3 days to dig 8 ditches, working at the same rate how long will it take 4 people to dig 10 ditches?
A: 5.625 days
18 people days to dig 8 ditches = 2.25 people days per ditch
10 ditches = 22.50 people days
22.50 / 4 = 5.625 days.
August 2019 Brain Puzzler Solution
Q: On an analog clock, how many times do a clock’s hands overlap in a one week period?
A: 154
At 12:00, the hands exactly overlap but not at other times — for example, at 1:05, the hour hand has moved slightly… and at 6:30, the hour hand is halfway between the 6 and the 7.
Making the times that they will overlap only 11 times in 12 hours (60 minutes /11).
12:00, 1:05ish, 2:10ish, 3:15ish, 4:20ish, 5:25ish, 6:30ish, 7:35ish, 8:40ish, 9:45ish, 10:50ish.
In one day they will overlap 22 times so in one week, 154 times.
