ahistegt4 Wrote:Guys, I have trouble solving a few difficult math question types, so I will post some questions that I made up myself.
I ll start with combinatorics:
Q: A dice with 10 sides ( :lol: do you care?!). You throw it 3 times. In how many ways the numbers add up to 12?
Please explain your answer constructively for everyones benefit.
making an organized list here is really not that bad, and it can easily be done within two minutes.
just arrange it by first throw.
IN ANY PROBLEM THAT OBVIOUSLY HAS TOO MANY STEPS TO "GRIND", START LOOKING FOR PATTERNS.
THEY WILL BE THERE.
PERIOD.first throw = 10 --> second + third throws = 2. there's 1 way to do this (i.e., 1, 1).
first throw = 9 --> second + third throws = 3. there are 2 ways to do this (i.e., 1, 2 and 2, 1).
first throw = 8 --> second + third throws = 4. there are 3 ways to do this (i.e., 1, 3; 2, 2; and 3, 1)
the pattern is clear.
there will be four ways if the first throw is 7; five ways if the first throw is 6; etc.
all the way down to ten ways if the first throw is 1.
1 + 2 + 3 + ... + 10 = 55.
done.
pattern recognition is king.