![lin550](/avatars/6417.jpg)
lin550
05.05.2020 •
Mathematics
Mario is making a sculpture out of stone.He starts by carving a base with five sides.He then carves five triangular lateral faces that all meet at a point at the top.What three-dimensional figure does Mario make?
Solved
Show answers
More tips
- C Computers and Internet The Twitter Phenomenon: What it is and How to Use it...
- C Computers and Internet How to Choose a Laptop: Expert Guide and Tips...
- C Computers and Internet How to Choose a Monitor?...
- H Horoscopes, Magic, Divination Where Did Tarot Cards Come From?...
- S Style and Beauty How to Make Your Lips Fuller? Ideas and Tips for Beautiful Lips...
- C Computers and Internet How to Learn to Type Fast?...
- A Art and Culture Who Said The Less We Love a Woman, the More She Likes Us ?...
- F Family and Home How to Get Rid of Your Neighbors?...
- S Society and Politics How Could Nobody Know About the Dead Mountaineers?...
Answers on questions: Mathematics
- M Mathematics 3 -gt a = Y 4 a = Submit Answer...
- M Mathematics Find an equation in standard form of the parabola passing through the points (1, -2), (2, -2), (3, -4)?...
- M Mathematics Given circle P, which of the following options best represents the macd...
- M Mathematics Which situation can be represented by 20s 30 + 14s? * A. Jeannie makes and sells personalized picture frames. She sells the frames for $20 each. She spends $30 for an electric...
- M Mathematics You know the drill people. FIX THIS NOW!!...
- M Mathematics 4m-2+(-8) EquIivalent expressions...
- M Mathematics What is the range of the function f(x) = {*1 – 3? 4 3 2 L all real numbers all real numbers less than or equal to 3 all real numbers less than or equal to -3 all real numbers...
- M Mathematics Since you guys said you couldn t see it last I reuploaded...
- M Mathematics A scientist needs 10 liters of a 20% acid solution for an experiment, but she only has a 5% solution and a 40% solution. To the nearest tenth of a liter, about how many liters...
- M Mathematics Kelvin measured the distance from his door to the park. It is 1.5 miles. The distance from Kelvin’s house to the library is twice the distance from Kelvin’s door to the park....
Ответ:
since each ball has a different number and if no two pairs have the same value there is going to be 14∗14 different sums. Looking at the numbers 1 through 100 the highest sum is 199 and lowest is 3, giving 197 possible sums
For the 14 case, we show that there exist at least one number from set {3,4,5,...,17} is not obtainable and at least one number from set {199,198,...,185} is not obtainable.
So we are left with 197 - 195 options
14 x 14 = 196
196 > 195
so there are two pairs consisting of one red and one green ball that have the same value
As to the comment, I constructed a counter-example list for the 13 case as follows. The idea of constructing this list is similar to the proof for the 14 case.
Red: (1,9,16,23,30,37,44,51,58,65,72,79,86)
Green: (2,3,4,5,6,7,8;94,95,96,97,98,99,100)
Note that 86+8=94 and 1+94=95 so there are no duplicated sum
Step-by-step explanation:
For the 14 case, we show that there exist at least one number from set {3,4,5,...,17} is not obtainable and at least one number from set {199,198,...,185} is not obtainable.
First consider the set {3,4,5,...,17}.
Suppose all numbers in this set are obtainable.
Then since 3 is obtainable, 1 and 2 are of different color. Then since 4 is obtainable, 1 and 3 are of different color. Now suppose 1 is of one color and 2,3,...,n−1 where n−1<17 are of the same color that is different from 1's color, then if n<17 in order for n+1 to be obtainable n and 1 must be of different color so 2,3,...,n are of same color. Hence by induction for all n<17, 2,3,...,n must be of same color. However this means there are 16−2+1=15 balls of the color contradiction.
Hence there exist at least one number in the set not obtainable.
We can use a similar argument to show if all elements in {199,198,...,185} are obtainable then 99,98,...,85 must all be of the same color which means there are 15 balls of the color contradiction so there are at least one number not obtainable as well.
Now we have only 195 choices left and 196>195 so identical sum must appear
A similar argument can be held for the case of 13 red balls and 14 green balls