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POTW #33 AND #34 Solutions...Fo real and NEW Questions by Popular Demand
Wow, a large number of you mentioned to me that you STILL want to have Math POTWs each week. You students continue to impress. Of course I will acquiesce.
POTW #35 Firstly, I think we already did this POTW before, but I'll just do it again regardless. The number of 3 digit positive integers from 100-999 is 900. From there, we have to find all in which the digit sum is 10. There are many different combinations of numbers to make 10, but in this case, I'll just list all the numbers needed. From 100-199, there are 10 outcomes in which their digit sum adds up to 10: 109, 118, 127, 136, 145, 154, 163, 172, 181, 190. From 200-299, there are 9 outcomes: 208, 217, 226, 235, 244, 253, 262, 271, 280. From 300-399, there are 8 outcomes: 307, 316, 325, 334, 343, 352, 361, 370. There's a pattern of the outcomes decreasing by 1 for every 100 intervals. It keeps on going until from 900-999, there are 2 outcomes: 901, 910. 10 + 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 = 54. 54/900 reduces to 6/100 reduces to 3/50 = 0.06 = 6%. The probability of getting a digit sum of 10 from a random 3 digit number is 3/50, 6% or 0.06.
Daisy built snowman with green scarf, top hat and four buttons. Delilah built snowman with blue scarf, earmuffs and two buttons. Donny built snowman with purple scarf, carrot nose and three buttons Duke built snowman with red scarf, flower and five buttons.
Fun in the Snow: Info: - Daisy's snowman has a top hat and one fewer button than the snowman wearing the red scarf, but one more button than the snowman with the carrot nose. - The snowman wearing the blue scarf, who is wearing the earmuffs has two fewer buttons than the snowman wearing the green scarf. - The snowman wearing the purple scarf has one more button than the snowman built by Delilah - The snowman built by Duke is wearing the flower.
This time, I did my work on paper instead.
Results: Daisy- Purple, 3, Hat Delilah- Blue, 2, Earmuffs Donny- Red, 4, Carrot Nose Duke- Green, 5, Flower
POTW #35
ReplyDeleteFirstly, I think we already did this POTW before, but I'll just do it again regardless.
The number of 3 digit positive integers from 100-999 is 900. From there, we have to find all in which the digit sum is 10. There are many different combinations of numbers to make 10, but in this case, I'll just list all the numbers needed. From 100-199, there are 10 outcomes in which their digit sum adds up to 10: 109, 118, 127, 136, 145, 154, 163, 172, 181, 190. From 200-299, there are 9 outcomes: 208, 217, 226, 235, 244, 253, 262, 271, 280. From 300-399, there are 8 outcomes: 307, 316, 325, 334, 343, 352, 361, 370. There's a pattern of the outcomes decreasing by 1 for every 100 intervals. It keeps on going until from 900-999, there are 2 outcomes: 901, 910. 10 + 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 = 54. 54/900 reduces to 6/100 reduces to 3/50 = 0.06 = 6%.
The probability of getting a digit sum of 10 from a random 3 digit number is 3/50, 6% or 0.06.
Daisy built snowman with green scarf, top hat and four buttons.
ReplyDeleteDelilah built snowman with blue scarf, earmuffs and two buttons.
Donny built snowman with purple scarf, carrot nose and three buttons
Duke built snowman with red scarf, flower and five buttons.
I do not know if I'm correct.
POTW 35 & 36:
ReplyDeleteI might do the sum probability questions after.
Fun in the Snow:
Info:
- Daisy's snowman has a top hat and one fewer button than the snowman wearing the red scarf, but one more button than the snowman with the carrot nose.
- The snowman wearing the blue scarf, who is wearing the earmuffs has two fewer buttons than the snowman wearing the green scarf.
- The snowman wearing the purple scarf has one more button than the snowman built by Delilah
- The snowman built by Duke is wearing the flower.
This time, I did my work on paper instead.
Results:
Daisy- Purple, 3, Hat
Delilah- Blue, 2, Earmuffs
Donny- Red, 4, Carrot Nose
Duke- Green, 5, Flower
That is Sum Probability:
ReplyDeleteTotal Answers: 54
109, 118, 127, 136, 145
154, 163, 172, 181, 190, 208, 217, 226, 235, 244, 253, 262, 271, 280, 307, 316
325, 334, 343, 352, 361, 370, 406, 415, 424, 433, 442, 451, 460, 505, 514, 523, 532
541, 550, 604, 613, 622, 631, 640, 703, 712, 721, 730, 802, 811, 820, 901, 910
You probably could have done this by either guess and check or multiplying or adding 10+9+8+7+6+5+4+3+2+1, but I got lazy and did it by Java. :)