Math Forum - Problem of the Week Submissions for Anh’s Code Student Short Answer Long Answer Student 1 The answer is 13 This was an algebra problem with characters for symbols instead of letters for numbers. In each equation I tried to figure out what each symbol stood for in a way that would answer that problem. By the time I reached the main expression I knew what the characters stood for. H is + S is / R is L is power B is x Student 2 Anh's group should get the answer 0.9375. Basically, the heart represents addition, the star represents division, the raindrop represents subtraction, the lightning bolt represents multiplication, and the bull's eye represents incrementation. The expression, not using the symbols, using plus, minus, times, divided by and increment, is this: 2 times 3 divided by (4 incremented by 3 minus 10) plus 6 times 2 incremented by (4 plus 1) divided by (1 times 4 incremented by 20). In the first bracket in the expression, you would do 4 bulls eye 3, which is 4+4+4, which is 12. Then, the next symbol is the raindrop. So, 12 raindrop 10 (or 12 minus 10) is 2. The first bracket is 2, so now our expression looks like this: 2 times 3 divided by (2) plus 6 times 2 incremented by (4 plus 1) divided by (1 times 4 incremented by 20). The next bracket is simply 4 plus 1, so this bracket is 5. Our expression is now: 2 times 3 divided by (2) plus 6 times 2 incremented by (5) divided by © 1994-2016 Drexel University http://mathforum.org/pows/ Page 1 of 14 (1 times 4 incremented by 20). In the next bracket, we would do 1 times 4 (4) then 4 incremented by 20 (80). So now our expression is: 2 times 3 divided by 2 plus 6 times 2 incremented by 5 divided by 80. 2 times 3 is 6, and 6 divided by 2 is 3 The expression is: 3 plus 6 times 2 incremented by 5 divided by 80. 6 times 2 is 12, and 3 plus 12 is 15. Now, our expression looks like this: 15 incremented by 5 divided by 80. Student 3 Student 4 Student 5 I found out ahh 'code and the bow eye is * and h is + and L ^and the r - and the s is ^ The answer for the problem Ahn's group made up to give to Aura's group is 13. The answer to 2L3S(4B3R10)H6L2B(4 H1)S(1L4B20) is 10. © 1994-2016 Drexel University http://mathforum.org/pows/ 15 incremented by 5 should equal 75, then 75 divided by 80 is 0.9375. Our answer should be 0.9375. Frist I think about the problem and look at the problem i realized there were 4 expones but there were 5 so I thought about the exponets i knew there were 5 so i took a guest about squaring and exponets susan said try it I tried and it work. First I had to find out what each symbol meant. To do that I just tried every math symbol to substitute for the symbols. After I finished 1 equation and had all of the right symbols I wrote the symbols down and it's correct mathematical symbol. After I finished finding all of the correct symbols I wrote out the big expression using mathematical symbols instead of the original symbols. These are the correct mathematical symbols for each of the original symbols: H=addition, S=division, R=subtraction, L=to the power of, and B=multiplcation. In the big expression I first of all had to do all of the parts in parentheses first. the first part in parentheses was 4*3-10. I knew 4*3 was 12 so I took 12 and subtracted 10 off of it giving me 2. The next part in parentheses was 4+1 which I knew was 5. The last part in parentheses was 1 to the power of 4 * 20. I knew that 1 to the power of 4 was 4 and 4 * 20 is 80. NOT DONE!!!!!!!!!!!!!!!!!!!!!!! On the first equation, I first guessed that the star signifies division. Then, I figured that the heart is addition, using the math fact 45/3=15. The second equation thus is (14/2R5)L2 =4, or (7R5)L2 Page 2 of 14 Student 6 They should get 1.125. =4. Only 2*2 or 2^2 fits that form, so the raindrop must be subtraction, and that the lightning bolt is either power or multiplication. I guessed that the lightning bolt was multiplication. That was disproved in the fourth equation, so 2L2 must be 2^2. The last one remaining for the bull's eye was multiplication, so 2L3S(4B3R10)H6L2B(4H1)S(1L4B20) is 2^3/(4*3-10)+6^2*(4+1)-(1^4*20), which, when solved, is 10. I figured out this: S=/ H=+ L=x R=b=x Student 7 I found that H=+, S=/, R=-, L=+, and B=*. Student 8 The answer to Ahn's expression is 9.623 Student 9 The solution to the expression is 13. The heart is a Addition symbol, the Star is a © 1994-2016 Drexel University http://mathforum.org/pows/ Student 10 Then I substituted these with operations. I found these by pluging in a sign for each problem then when i got that one i plugged in the known one for the next problem. and then for the last problem i pluged in the signs that i had found and i got 9.623 for an answer for that problem. H=+ addition S=/ division R=- subtraction L=+ addition B=X multiplication I just looked at the problem and decided what the logical reasoning would be. I substituted the symbols with different mathematical operations. It was basically guess and check. Then for the last one i put it in my calculator and got the answer The heart (H) is equal to addition, the star (s) is division, the raindrop (R) is subtraction, the bull's-eye (B), is multiplication, and the Lightening bolt (L), means the number before it is raised the the power of the number after it. To get this answer, I tried different operations to see which ones made the equations mathematically correct. (5+40)/3=15 (14/2-5)^2=4 4*(14-6)*2=64 Therefore the equation is 2^3/(4*3-10)+6^2*(4+1)/(1^4*20). Guess and check is what i did the whole time. Page 3 of 14 Student 11 Student 12 Student 13 Student 14 Student 15 Division symbol, the Raindrop is a subtraction symbol, the lightning bolt is an exponet symbol, and the dot is a multiplication. The following codes for anh's code is H=addition,S= division, R= subtraction, L=exponent, B= multiplication to solve the problem. h is equals additon star equals divison raindrop equals subbtraction lighting bolt equals exponet and bullseye equals multication I tried all operation signs which I had to use most of and that's ow I found my answer. These are the codes that you need to solve Anh's code: H=addition S=divison R=subtraction L=exponent B=multipaction My answer came to H=addition S=division R=subtraction L=exponent B=multiplication © 1994-2016 Drexel University http://mathforum.org/pows/ I tried to solve the problems in different ways to see if the code matches with the answer. So I might have tried for the first equation 5x40 and then 5-40 and ect. and tried all those numbers with the symbols. It was complicated at first but then it got easier. Because i kept using the same system for all the numbers. The answer for AURORA'S GROUP. is 13. I got all the codes (ex. the heart and star ect.), and tried solving the equation like I wouldv'e done with another equation. and I got the answer. Well it was very easy all you need to do is figure out what the symbols mean and you will know the answer. The symbols was process of elimation. I tried all operation signs which I had to use most of and that's ow I found my answer.What I did t find my solution was I took the problem and I tried all operations of math multiplication, division and such and when it looked right to me that was my outcome answer. I solved this problem by just trying different opperations til I could get an awnser for one problem. So I would just do the first one by trying the different awnser. Then I will do the next one and use some of the same operations. I came up with this reason by working out the problems trying all different operations and seeing which one worked. By doing that, I seen which one fit the equation that would make it result in the correct answer. That is how I came up with the answers. Page 4 of 14 Student 16 Student 17 Student 18 H=addition,S=divition, R=subtraction,L=multi palcation,B=exponent My final solution is 13. H=+, S=division, R=-, L=exponent, B=x. The answer to the expression is 13. First i tried to put in anything just to see if it would work and i was suprized because it did work. So just to check i did another problem.and it was correct....lol,,dont ask Well I really only used guess and check, but most of the problem came to me naturally. I found my answer by continuously changing the signs and seeing which best fit. Once i found that H=+, S=division, R=-, L=exponent, and B=x i saw that all the equations worked out: (5+40)divided by 3=15 (14 divided by 2 - 5)to the second power=4 4x(14-6)x2=64 For the expression: First i put in the signs: 2to the third power divided by (4 x 3 - 10)+ 6 to the second power x ( 4 + 1 )divided by (1to the fourth power x 20) Next i did the problems in (): 2to the third power divided by (2)+ 6 to the second power x (5) divided by (20) Then i did the exponents: 8 divided by 2 + 36 x 5 divided by 20 Then i did all the division and multiplication: 4+9 Finally i came up with my answer: 13 Student 19 I belive that the answer to Anh`s code is: heart is additon, star is division, raindrop is sudtraction, the lightnig bolt is exponet, and the © 1994-2016 Drexel University http://mathforum.org/pows/ I did the problems on the top but did not under stand what exactly to do at the bottem. Page 5 of 14 Student 20 bull`s-eye is multiplacation. H=ADITION,S=DIVISIO N,R=SUBTRACTION,L=E XPONENT.AND HE B=MULTIPLACATION Student 21 H is +, S is division, R is -, L is exponent, B is x. Student 22 Heart=addition Star=division Raindrop=subtraction Lighting=exponent Bull's eye=multiplication Student 23 H is + S is / R is - L is ^ B is * Student 24 I do not have an answer because I did not really understand how to solve it. The way that i came up with the answer was by trying out all the soutions, and seeing if they came out to be what the right answer at the end of the problem. Tha H=adition,S=division,R=subtraction,L=exponent,and the B=multiplacation First I solved the first problem. I tried different things for the heart. Then I came up with a + sign. So I knew all the other hearts were +. Then it would be 45. Then I did 45 divided by 3=15. So I knew that the star is the division sign. Then I went to the second line. I already knew that the star was was the division sign. So I tried different things for the raindrop. Then I noticed that it would be the - sign. Then the I used the exponent sign for the lightening bolt because the problem make sense. Then the last problem had the bullseye and the only sign left was the x sign. So I filled it in and the problem made sense. For the first oparation I thought that the heart was division because the answer was a small number. I figure that it didn't work so I keped on looking for the right one so the only one that worked was adding 5+40=45 and 45 divided by 3 and it was the right answer. I did the same with all of the trying to match it with the correct answer. Thats how I got all the right answers. What I did on the first problem was made the heart + because 5+40 equals 45. then after that I made the star / because 45 / 3 equals 15. on the second problem the star stays / and i made the raindrop because 14 / 2 equals 7 - 5 equals 2. when I was done doing that problem I made the lighting bolt ^ which made that problem 2^2 equals 4. then on the thrid problem I made the bulls eyes * and the raindrops stayed - which made the problem 4*(14-6)*2=64. the last problem came out to 13 the way i got 13 was i did the ()first from left to right and the the ^ then the * and / from left to right then i did * and - left to right and i got 13. I am not really sure of what the symbols mean. Would you explain to me how to figure out the expression in the middle of the page? Thank you for your help. © 1994-2016 Drexel University http://mathforum.org/pows/ Page 6 of 14 Student 25 Student 26 Student 27 first i added than i mulitiplyed than subtracted and divided the answer which gave me these answers first I added,subtracte,and multiplied. h=+, S=division, R=-, L=exponet, B=x. The answer to the expression is 13 Arron fisrt i added 5and 40 divided by 3which is 15 for the second one i got 14 divided 7-5to the 2second power=4 for the thrid one i got 4x14+6x2=64 bouns:2to the 2second power3divided by 4to the first 1power 3 -10+6 to the 2second powerand 2 to the second powerthan 4=1divided by 1to the second power4to the first power20 first i added for the first one 5X40divided 3=15 for the second one i got 14divided 7-5to the 2 to second power=4 for the third 14x4+6+2=64 for the very last one i got 2to the second power3divided by 4x3-10+6to the secondpower2-4+1 divided 1 divided to the second power4 1 20 Anh's group First I tryed to figure out the first line (5h40)s 3=15. I came out with verious conclutions, so i did the second line (14 s 2 r 5)L2 +4. It took me a little while but i figured out out that s= the division signed because it worked out on evry other star. To that i did the rain drop next and it would only br a minus, and the only thing left for that problem was a L and i relized it was an exponite. 14 divided by 2-5 2 to the second power +4 Then i went back to the first one i there knew that the h=+ because 5+40=45 and 45 divied by 3 is 15 so that worked out easily. For the last problem the only opperation left was times so i knew it was the bulls eye because the raindrop was alredy a - sign and the hole thing worked out right Aurora's group i stared with the prenticys first and got 2 one and 5 for the second and 20 for the last one. The i worked my way out from the left to the right.It was my kinda hard but i came up with the solution 13 © 1994-2016 Drexel University http://mathforum.org/pows/ Page 7 of 14 Student 28 The here is what each letter equals H equals + S equals / R equals L equals exponent B equals * Student 29 the heart represents the adding symbol,the star represents the division symbol,the raindrop represents the suntraction symbol,the lightning bolt represents the exponent symbol and the bull's-eye represents the multiplication symbol. These are the answers that i got H=addition, S=division, R=subtraction, L=exponent, B=multiplication The H=+, the S=Division, the R=-, the L=Exponet, and the B=Multiplication. Student 30 Student 31 The way I figured it out is by first solving the first problem like this first I added 5 to 40 and I got 45 then I divided 3 into 45 and I got to 15 then I went to the second one and I already know I have to divide 2 into 14 out of that I got 7 so then I knew the only way I could get to 4 is to subtract then I got 2 so I put the other 2 into the 1st power since I knew that when you put 2 variables together you have to multiplie so that how I got 4 so I pretty much knew that bull's eye was the exponent over all I thought this was a fairly hard problem because I didn't know if it was a 1st power The first thing that i did was try to figured out how they found the asnwer for the first problems that you put.For each symbol i tried every math problem till i got the one that it was.It took a little bit of time and of thinking to find what the symbols meant in the first part.But everytime i got one symbol solved it was easier to find the next one. I got my answer by using different kinds of combinations with the numbers until i got the correct answer To get my answers I tryed solving the first problem. (5 H 40)S 3=15 First I replaced the H with + and I solved that first and that gave me 45.Then I had to figure out what the S is and I figured that out by taking the 45 and Dividing it by 3 and that gave me the correct answer of 15. (5 + 40)Divide 3=15 (14 S 2 R 5)L 2=4 For this problem I took the information that I had used from the last problem and used it in this problem. (14 Divide 2 R 5)L 2=4 Since I knew the S was Division I placed it where needed to be and © 1994-2016 Drexel University http://mathforum.org/pows/ Page 8 of 14 solved the problem. 14 Divided by 2=7 (7 R 5)L 2=4 First to get the answer to the rest of the problem I tryed putting where the R was. (7-5)=2 2 L 2=4 In this problem you could have used multiplication or exponents.I tryed using the multiplication frist but that proved to be wrong in the third problem, so then I went back and used exponents instead. 2 To the 2nd Power=4 4 B(14 R 6)B 2=64 I replaced the R with - because that's what I got from the previous problems. 4 B(14-6)B 2=64 (14-6)=8 4 B 6 B 2=64 Then I replaced the B with the only possible thing which was Multiplication. 4 Multiply 6 Multiply 2=64 Student 32 The solution i acquired for this problem is 13. 2 L 3 S(4 B 3 R 10)+6 L 2 B(4+1)S(1 L 4 B 20) I placed everything where it needed to be and then I tryed my best to solve it. 2 to the 3rd power divide(4 Multiply 3 - 10)+6 to the 2nd power Multiply(4+1)Divide(1 to the 4th power multiply 20) The answer that I got to this was 6.6. I started out by finding what the value of each symbol was. I found the value of the symbols by solving each equation Anh left for Aurora. My answer for each symbol is: H= Addition S= Division R= Subtraction L= Exponent B= Multiplication Once i knew which symbol stood for which mathematical operation i replaced the equation and came up with this: © 1994-2016 Drexel University http://mathforum.org/pows/ Page 9 of 14 (2 to the third power)divided by (4x3-10)+ (6 to the second power) x (4+1) divided by (1 to the fourth power x 20) So i followed the rules for multiple-step equations and started by solving the parenthesis firsts, then the exponents, then multiplication or division (whichever came first) and then Addition or Subtraction (whichever came first) and ended up with: (8 divided by 2)+ (36 x 5 divided by 20) And finally: 4 + 9 = 13 Student 33 Student 34 Student 35 Student 36 . I ended up figuring that H=addition, S=division, R=subtraction, L=multiplication, and I thought that the bullseye=exponents The answer I got was addition for Heart(H),multiplication for Bull'seye(B),division for star(S), subtraction for raindrop (R),and last expotents for Lighting(L). i subtracted added multiplied and divided h=addition s=division r=exopents l=mulitipy b=subraction © 1994-2016 Drexel University http://mathforum.org/pows/ I came across that when I was trying to complete the problems at the top. How I got the answer for these different equations were putting in different types of symbols. I thought thta the fist two were very easy becasue I first tried to put addition and subtraction and it worked. So I went on to the next problem which also was easy. The exponent and the subtaction and I also knewed that the S was a division sign so I plugged that in. After finishing all the problem I tryed to slove it over again to make sure they were fitting in propaly and it did so I wrote the problem over again and got thte answer.In hte beginig I did mess up but then I figured that I had to switch the symbols up of expontens and multiplication. I was finished and a teachered looked over it and said that it was correct. I liked doind these kind of problems a lot because I'm very good at operations. i did the math and found out the exponents Okay i think I Got it Now i Have H=addition S=division Page 10 of 14 Student 37 Student 38 Student 39 Student 40 I found that (H)=Addition (S)=Division (R)=Subtraction (L)=Exponets (B)=Multiplication. the following shapes equal an operation:h=+,s=diviso n,raindrop=(),l=exponet,and b=* The heart is addition, star is division,raindrop is subtraction, lightening bolt is an exponent, and the bull`s eye is multiplication.For the long expression is thirteen. H=Addition R=Subtraction S=Division L=Exponents and B=Multiplication and then I got 25 for the final answer. My Final answer for this Problem, For H i got addition. For S i got Division. For R i got © 1994-2016 Drexel University http://mathforum.org/pows/ Student 41 R=subraction L=exponents But I Try Bulleyes And ?Its Still Not Working I started with problem number one because i thought it was easier than the others. so when i first started i just put any math symbol and tried to solve the problem if that didn't work than i tried another one and so on until i finally found one that worked. and i continued with the problem and found out the other ones. first i started with sloving the 1st equataion. i just took the 5 operations and just started sloving the equation wit the different operations. when i finally got the answer of h=(+) and the s=division. i went onto the 2nd eqation. the s=division,r=(-),and l=multiplcation. when i wen on 2 da 3rd equation i found a mistake. i found that 1 of my operations on the previous equations was wrong. it was the lightening bolt, instead of mulitiplcation it was an exponent. i found that by trying the last 2 operations i hadnt used yet,which was exponents and mulitiplcation.for the last big final equation i got the number 13 We took one problem at a time and tried different equations for each problem.We knew that the exponent would be the number by its self.It was even harder because you had to follow the order of opperation. The first two where easy but then we had to go back, and change our answer because it didn`t come out right for the third one. The process that I used for this problem was guess and check at first I did the first problem and I got addition=H and disision=S so after that I put those for the rest of the symbols in the other problems. Then for the next problems I had to guess for the other symbols and that's when i guessed R=subtration,l=exponents and B=multiplication.But it took me awile before I put them with the right symbol.Basically, I just did guess and check for all of the problems and when I got to the end I got 25 for the final answer. (5+40)divided by 3=15 (14 divided by 2-5) (2 to the second Power)2x2=4 4x8x2=64 Those are some of the examples i got for my problems, I hope you Page 11 of 14 Student 42 Student 43 Student 44 Student 45 subtraction. For L i got exponets, and for B i got multiplication. For the bottom i got 10! They should get 13 as their answer. heart is addition,star is divison,raindrop is subtraction,lightning is exponents,bulls eye is multiply.i diddn't find put the long problem at the bottom of the page h/addition s/division r/subtraction l/exponent to the second power b/multiplacation (5 plus 40) divided by 3 = 15 (14 divided by 2 minus 5) multiplied by 2 = 4 4 2 to the 2nd power (14 minus 6) 2 to the 2nd power 2 = 64 2 plus 3 divided by (4 2 t I got plus for the heart, for star I got division, for the raindrop I got subtraction, and I got times for bulls eye, I also have an exponent for the lightening. © 1994-2016 Drexel University http://mathforum.org/pows/ uderstand them. To slove it i used my brain and my calculator. I no that 5+40=45 so 45 divided by 3=15 If you could explain an easier way to do it I would love that. I got that answer because I figured out that the H=addition, the S=division, the L=exponents, the R=subtraction and the B=multiplication. i took me about 20-30 minutes to find out the answer but i finally go it right.I had 2 other people in my group. [h]heart [s]star [r]raindrop [l]lightning [b]bull's eye (5 h 40)S 3=15 (14 S 2 R) L 2=4 (4 B (14 R 6) B 2=64 The problem gives you numbers with symbols and you have to try to figure out what they are to solve each part of the problem.For example: 5#5=15.The process I used to solve the problem was guess and check.Like I would try all of the mathematical operations until I would get the answer already showing on the paper.Then if I couldnt get the correct mathematical operation on a certain line of the problem I would try the next line and if it was correct I would try the same operation on the line before. I looked at the answer and I saw that it was 15 so i tried to times 5 by 40 but then it didnt work then I tried to subtract and it wouldnt work so I added it then I put a divison sign where the star was then I came up with the answer 15. The second problem I put a division sign and I got subtraction for the lightening I put an exponent I got the exponent because 14 divided by 2 subtract 5 equaled 2 and I put the other 2 as the exponent then I got 4 for the answer. For the ater problem I already had the bulls eye as times and the raindrop for an subtraction and the other bulls eye was times and it equaled 64. At Page 12 of 14 Student 46 Student 47 he answer is the heart is addition,the star is divison,the raindrop is subraction,the lighting is exponents and the bulls eye is multiply.the awswer should come to be 367. H-addition, Rsubraction, S-division, L-exponents, and Bmultiplication the bottom I put 2 to the 3 power divided by 4 times 3 subtracted by 10 plus 6 to the second power times 4 plus divided by 1 to the 4 power times 20 and for my answer I got 13. i got this answer by multipling and dividing it took me about proably ten minutes or about twenty minutes,i tryed on problem and i hope it right. the heart is [H] the star is [S] the raindrop is [R] `the lightening bolt is [L] the bull's eye is [B] I first tried addition for heart because I thought it was the eastiest to start with . Then the problem statrs to form. I came up with S being divison becasue he just came to my head it might be like that. After I finish with the first row I put the ones I all ready know inside the problem. I saw which ones I had left so I started to put in the other operations. When I finish with everything it looked like this. (5+40)/3=15 (14/2-5)L2=4 4*(14-6)*2=64 Student 48 Student 49 the H is addition and the S is dividion and the R is subtraction and the L is exponets and the B is multiplcation The star is division, the heart is addition, the tear drop is minus, the lightening bolt is exponents and the bull's-eye is multiplication. © 1994-2016 Drexel University http://mathforum.org/pows/ so the answer to the equation is 13. First we took the five H fourty and s three and we equal up two fifthteen the second we had fourteen S two R five exponetstwo and I got four and then third we took four B fouyrteen R six B two and equal up two sixty four and the the last probelm we two exponets three S four B three R ten H six exponets two B four H one S one exponets four B twenty and we equal to eighty While figuring out this problem I was working with the first clue. I got the H by trying all the trying out all the different operations , I knew it couldn’t be multiplication because that would make the answer higher so first I tried addition and I knew that could be a possible answer , so I tried the addition with division and came out right. (5+40) divided by 3 = 15 first I did the addition 5+40= 45 then I did the division 45 / 3 = 15, so the first problem was right. Then I worked with the second problem to see if the division was right. And it was, so then I tried and Page 13 of 14 Student 50 heart is addition, star is division, raindrop is subtraction, lightning is exponents, and the bulls eye is multiply. figure out what the other ones were with division and addition out of my way I knew the rest how to be either exponents, multiplication or minus. So I tried the T as minus and the L as exponents. (14 divided by 2 – 5) 2 to the second power= 4. First I took 14 divided by 2 = 7 then I subtracted 5 = 2 x 2=4, which is the answer. Then I worked on the third problem 4x (14-6) x2=64 first I did the problem in the parenthesis which equals 8 then I took 8x4 = 32 then 32x2 = 64 which makes the symbols all right. Although I didn’t figure out the last equation yet I am working on it with the calculator. it took me a long time to figure out the answer but i finally found it out the heart(H)is addition, the star(S)is division, raindrop(R)is subtraction, lightning(L)is exponents, and the bulls eye(B)is multiply. (5 H 40)S 3=15 which is (5+40)%3=15 (14 S 2 R ) L 2=4 which is (14%2-5)to the power of 2 2=4 4 B (14 R 6) B 2=64 which is 4x(14-6)x2=64 2L3S(4B3R10)H6L2B(4H1)S(1L4B20) which is 2to the power of 2 3%(4x3-10) +6to the power of 2 2 x(4 +1)%(1to the power of 2 4 x20) which equals to well inever got the answer because it took to long and class was over so i never got to finish and i started geting confused © 1994-2009 Drexel University http://mathforum.org/pows/ © 1994-2016 Drexel University http://mathforum.org/pows/ Page 14 of 14