POTW #10 Question:
It is more like a number riddle, but logic is at play here! Make the below equation true!
POTW #9 Grade 8 Answer:
POTW #9 Grade 7 Answer:
Thursday, November 9, 2017
POTW #10 - Student-Created!
Thanks Fiona for this week's POTW, and thanks to all the students for an AMAZING day today at St. Marie Among the Wendats.
POTW #10 Question:
It is more like a number riddle, but logic is at play here! Make the below equation true!
POTW #9 Grade 8 Answer:
POTW #9 Grade 7 Answer:
POTW #10 Question:
It is more like a number riddle, but logic is at play here! Make the below equation true!
POTW #9 Grade 8 Answer:
POTW #9 Grade 7 Answer:
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Grade 7 POTW
ReplyDeleteI'm just going to list the equation, that is literally the only fact.
Choo + Choo = Train
Well, there are many answers, I might calculate how many answers there should be in total in another comment for this reply, but first let's answer the question.
I know that the thousands place MUST be 5 or more. If it's 4, then there can't be a ten thousands place because 9 is as far as it can go. From there, any digits can work as long as this rule is followed and the logic of what variables mean is followed. To make the equation more understandable, I will change the equation a bit.
2 x Choo = Train
The thing is, variables can be the same digit so that is why it's simple. However, I WILL try to find different variables just to make it harder. I don't really want to leave it at that. Here are some more things to know.
o x 2 = n
o x 2 = ##
o x 2 + 1 = i
n + 1 = i
h x 2 + 1 = a
Okay, that means "o" is 5 or more. I'll say 5 just to see.
Ch55 + Ch55 = Tra10
I'll use 6 next for h just to try it out.
C655 + C655 = Tr310
C can just be something like 8 (5, 6 is a no and 7 would result in another 5).
8655 + 8655 = 17310
There's a problem. 1 would always be the ten thousands and I didn't realize until now.
t=1
Let's change it up a bit.
8766 + 8766 = 17532
BINGO!!!!!!!!!!!
Choo + Choo = Train
8766 + 8766 = 17532
C = 8, H = 7, O = 6, T = 1, R = 7, A = 5, I = 3, N = 2 are the variable values. Replacing these makes the sum true. Once again:
BINGO!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! (That's my answer)
Grade 8 POTW (I said grade 7 before by accident, mind as well say 8 now)
ReplyDeleteOh wait! I sent too soon. I just realized I used two 7s (I think). Let me continue on.
Okay using the other things I knew. I'm just going to continue.
T = 1 still so that is important. 5 can't be it because it defies the fact.
Ch66 + Ch66 = 1ra32
I'm going to use a value for "a" that doesn't result in another value already used. 0 can't work because it'll go to 1 which is already settled upon. 1 goes towards 3. I'll use 3 is already used too. I'll use 4.
C466 + C466 = 1r932
Once again, 0 can't be used. 1, 2, 3 and 4 can't be used. I'll use 5
5466 + 5466 = 10932
Choo + Choo = Train
It's either I just got another answer and just re-did it, or what I think I really did, use 7 twice. I'll just let you see which values are which letters. Just compare top to bottom.
Choo + Choo = Train
5466 + 5466 = 10932
Ignore my re-doing lately (For now on, I WILL double check (I need to at this point))
I'm going to try and find more solutions. I know that there is more than 1.
Delete5466 + 5466 = 10932 is 1.
I'm going to continue on from there (previous solution).
77 for oo won't work because then 4 will be used for n when it's already used for h.
88 might.
5488 + 5488 = 10976
DOUBLE CHECK
5 is c. Is there a place value of 5 in train (10976). No. 4 isn't a digit either in 10976. 8 is also used once in 10976. Okay, this is another answer.
Choo + Choo = Train
5488 + 5488 = 10976
I will continue in another reply for more answers.
I now have 2 answers. There are most likely more because the only thousands digit I used was 5. Now to finish 5.
Delete5499 + 5499 = 10998
9 is used for many variables other than o. T is still 1 and o is more than 5.
Here is what I said before to make it easier.
o x 2 = n
o x 2 = ##
o x 2 + 1 = i
n + 1 = i
h x 2 + 1 = a
6h77 + 6h77 = 1ra54
For h, 1 can't work because it is taken, 2 can't work because then 5 is used again, 3 makes 7, 4 is already used, 5 is already used, 6 is taken, 7 is taken, 8 results in 7, 9 results in 9.
6hoo + 6hoo, o can't be 8 because the result makes n 6 when it is taken. The second o can't be 9 (right to left) because that will result in 9 after 9 + 9 = 18 + 1 from the previous.
7hoo + 7hoo = 1rain
7h66 + 7h66 = 1ra32
0 results in 1, 1 is used, 2 is used, 3 is used, 4 might work?
7466 + 7466 = 14932
Nope.
5 results in 1, 6 is used, 7 is used, 8 results in 7, 9 results in 9. Doesn't work.
8hoo + 8hoo = 1rain
8h66 + 8h66 = 1ra32
1, 2, 3 don't work. 4 might.
8466 + 8466 = 16932
Sadly NO.
8h77 + 8h77 = 1ra54
0 results in 1, 1 is used, 2 results in 5, 3 results in 7, 4 is used, 5 is used, 6 results in 3. That may work.
8677 + 8677 = 17354
So close.
For o, 8 is used for c and 9 will result in 8 and 9 again.
9hoo + 9hoo = 1rain
9h66 + 9h66 = 1ra32
0, 1, 2, 3 don't work. 0 will result in a repeated 1 and the rest are used.
4 results in 9, 5 shows 1, 6 is used, 7 results in 5. 7 could work.
9766 + 9766 = 19532
Doesn't work, but the thing is, r must be 8 or 9 and it can't be 9. r is 8 if it could work.
9hoo + 9hoo = 18ain
8 is used and 9 is used. I tried all logical ways that could work using the facts. In conclusion, the only possible answers include:
Choo + Choo = Train
5466 + 5466 = 10932
5488 + 5488 = 10976
I know these are the only answers for sure. I used trial and error for all ways (that have possibility of working). I really thought there would be more answers (unless I made a mistake and missed some answers).
Seayrohn said "I'll use 3 is already used too. I'll use 4"
DeleteI meant to say "3 is already used too..."
Grade 7/8 POTW:
ReplyDeleteSo I found 3 answers for this riddle.
5466+5466=10932
and
5488+5488=10976
and
6489+6489=12978
There is definitely more answers but I feel like three is enough.
6489 and 12978
DeleteYou used 8 and 9 for both train and choo. 6489 + 6489 = 12978 isn't a solution.
Cindy, "definitely" is a strong word. Are you sure there are more?
DeleteI'm pretty sure it says o twice. Can you use two different values for o?
Deleteo must be the same.
Delete12354+12354=24708
ReplyDeleteYou used 2 twice
Delete12354 is also a 5 digit number so it doesn't work.
Delete5466 + 5466 = 10932
ReplyDeletethis works since all the numbers should be different besides 00 in CHOO. 00 should be two of the same number and 0 + 0 = a two digit number since the total answer is one digit bigger. 66 works so I went with that. the first digit has to be bigger than 4 since the answer would still be a 4 digit number. Then I tried a couple of other solutions with 5_66 in order for it to work finally got 5466
Since I made this, I can't answer it since i know the answer. :D
ReplyDeleteGrade 7 POTW:
ReplyDeleteAs there is only one fact (which is the equation) I'm going to list it.
CHOO + CHOO = TRAIN
Now I know that as there are only a few repeating numbers (C, H, and O) then all the other numbers must be different. I also know that the "T" in TRAIN must be 5 or more, because if it's under 4, than it would not be able to create a number in the ten-thousands.
As I know the first number must be above 5, I'm going to start with 5. So, I now already know the first number.
5HOO + 5HOO = TRAIN
What I also know is that the "O"s must be the same, which then has to add to a different number that hasn't been used. Already, I have a wide variety of numbers I can use, as the only number that has been used is "5", and "5" is a prime number. However, I did have a way to decide what number to use. "OO" in "CHOO" should be two of the same number, and since the total answer is one digit larger (TRAIN) I assumed that it should be at least above 5. I decided, in the end, to use "8".
So now, my equation looks like this:
5H88 + 5H88 = TRAIN
The last letter (H) no longer has a wide variety of numbers I can choose from. To narrow it down, I will add what I already have to replace some of the letters in "TRAIN" - this way I will have an easier time of picking the last letter.
5H88 + 5H88 = 10A76
As I have not figured out "H", I cannot figure out "A". However, I do know which numbers I cannot use for both now, which are "5", "8", "1", "0", "7", and "6". The numbers that are left are "2", "3", "4", and "9".
I know, since I made "TR" into "10" that anything I have must NOT be over 5. That doesn't narrow it down much, only excluding "9" as a possible option. Let's talk about "2", then - if I add 2 and 2, that equals 4. However, because of 8 + 8 (in the equation) it would equal 5 instead, which is impossible. (8 + 8 = 16). Next, there's 3 + 3. However, 3 + 3 equals 6, which even then is impossible. When the 1 is added and it becomes 7 (again, from 8 + 8) that's still not possible. The only option left is 4.
Therefore, now the equation looks like this:
5488 + 5488 = 10976
(P.S. I'm sure that there are many other possible answers, but I only listed one of these many.)
I think it's just 2. I tried pretty much every logical solution in my answer comment and there were only 2.
DeleteTry using 6 instead of 8 for o to get the other possible answer!
DeleteAlan. You don't give away the answer. Let them try themselves, and if it is really necessary, then they'll read other comments. But yeah, use 6 and you'll get the ONLY other answer.
DeleteI got 2 answers which are:
ReplyDelete5488+5488=10976
and
5466+5466=10932
These equations work because its the same numbers you are adding which represents CHOO+CHOO. These are the same letters so the numbers have to be the same.Also, in CHOO, the last 2 O's are repeating, so the last 2 digits of the number have to be the same. And that works. The rest of the letters are C, H, T, R, A, I, and N. These are all different letters, so the rest of the numbers have to be different. And looking over the numbers you can see that it is true. I'm pretty sure there are other answers to this question but I only listed these 2.
I don't think there are more. My answer shows that I tried every logical possibility.
DeleteHmmm, let's see. I guess I was a bit late for this week's POTW and many people have said their answers already!
ReplyDeleteFirst of all, I started off with trial and error, and went with one digit a time to figure out my two solutions. This way, once I correct each digit, I was easily able to figure out two solutions, 5466+5466 = 10932(No repeated digits) and 5488+5488 = 10976.
After that I thought: Would there be more?
I didn't really want to sit there and guess and check for an hour to see if there was anymore. I was also reading the controversy between everyone saying that there is probably more possibilities and Seayrohn replying to every single comment saying that there are probably not anymore. So, I decided to check for myself.
I started off using a bit of guess and check, using the same strategy I used before, and replacing numbers on the way. All of my answers returned negative, which was at the point where I gave up and just set a computer running for less than a minute. It gave me the exact same two answers: 5466 and 5488. This way, I can realize that my coding was probably right since it gave me the two answers that I figured out already, but it didn't give anymore, which is also probably right because I let the computer test each possible number combination(Brute Force). So, these are the only two answers, and I think it is safe to say to trust my (*ahem totally good) coding this time.
-Alan
Hey! You use computers, I use my own one by one process. And it did take like an hour I believe!
DeleteGrade 8 POTW:
ReplyDeleteC = 5
H = 4
O = 6
N = 2
I = 3
A = 9
R = 0
T = 1
Work was done on paper.
GRADE 8 POTW:
ReplyDeleteThis was a run little riddle to complete! The way that I thought of this was by organizing info. First off it is 2 identical numbers (with the ones and tens being the same) that add up to a 5 digit number with no repeating numbers.
Rules I used as benchmarks:
-FOR TWO 4 DIGIT NUMBERS TO MAKE A 5 DIGIT NUMBER WE NEED THE TWO NUMBERS TO BE ABOVE 5000.
-FOR THE ONES AND TENS TO ADD UP AND MAKE TWO DIFFERENT DIGITS (within the 5 digit number) IT NEEDS TO BE ONCE AGAIN 6 AND OVER (assuming we use 5) SO THE CARRIED ONE IN THE TENS COLOMN CAN BE ACT UPON
using that method i guessed and checked;
one possible answer is 5466 + 5466 = 10932
One solution is 5488+5488=10976. I did the work in my math book
ReplyDeletePOTW:
ReplyDeleteSo first of all, I would like to give Fiona props for the really cool riddle for this week! Very creative =)
Now, I came up with two answers for this riddle, however there are probably other solutions. To find my solutions, I first needed to set some guidelines for myself when choosing the numbers.
- I know I can't use a number more than once if the letter doesn't appear more than once
- The numbers being added together had to be four-digit numbers and the product had to be a five digit number
- The equation had to actually work, meaning it had to make sense
With these parameters, I started guessing and checking my work, which is when I realized that the number had to be over 5000, as otherwise the product wouldn't be a five digit number. That realization helped as it narrowed down my options, which is when I came up with these two results...
CHOO + CHOO = TRAIN
5466 + 5466 = 10932
5488 + 5488 = 10976
Those are my two answers!
C=6
ReplyDeleteH=1
O=7
6177 + 6177 = 12000
T=1
R=2
A=3
I=5
N=4
At first the riddle was very open-ended. The only necessary components to this question is that CHOO must be above 5000. This is because in order to have 5 digits, the number must be at least 5 digits. Since in CHOO there is two Os, the two must be the same number or value. The sum must all have different numbers as all the letters are different as well. Even though there is a very wide range of possibilities for what TRAIN is in numbers, I decided to use 6177. This is just one of the numbers I thought of that works in the question.
1 is used twice (H and T)
DeleteUpdate the sum in the numbers is 12354, not 12000.
ReplyDeleteGrade 8 POTW:
ReplyDelete5466+5466=10932
C=5
H=4
O=6
T=1
R=0
A=9
I=3
N-2
Grade 7 POTW:
ReplyDeleteSo our equation here is:
CHOO
+CHOO
TRAIN
I liked to break this equation down based on how it was lined up by doing:
C+C=TR
H+H=A
O+O=I
O+O=N
Of course if there was regrouping in the equation from the previous place value then I would add 1 to the next equation.
So when doing addition that may have a chance of requiring regrouping, we all know we have to add the ones, then 10s then all the place values after that. Well from looking at this, for adding the ones and the tens both equations are O+O. However, there are different answers as with the ones O+O=N but with the tens it equals I. This means that O>4 because if a digit is 5 or more, regrouping is necessary so doing trial and error, I decided that O=6, ready to change it if it doesn’t work out. 6+6=12 But 6+6+1(regroup)=13.
I figured that C=5 as in the equation when broken down is C+C=TR and 5+5=10. This makes C=5, T= 1 and R=0
Now to see what H is equal to. Looking at the equation.
I see that 1+H+H=A as when it is lined up, the Hs and As are in the hundred sections. However, the 1 is important as seen in the tens place. O(6)+O(6)+1(regrouping from the ones place)=13 which >10 so we are regrouping in the hundreds section. So we now have H+H+1= I. Here the only restrictions we have is that neither H nor I can repeat a number. As the digits taken are 5,1,0,6,2,3. This leaves 4,7,8 and 9 left for the equation H+H+1=A.
4 is the only number under 5 and the kinky one that can be added to itself and 1 without regourping and going over 9. H+H+1= making it 4+4+1=9. Therefore, H=4 and A=9
Now that we have solved every letter, let’s mush it together and see what our answer is:
CHOO
CHOO
TRAIN
5466
5466
10932
This comment has been removed by a blog administrator.
DeleteThis comment has been removed by a blog administrator.
DeleteGrade 8 POTW:
ReplyDeleteCHOO = 5466
+ CHOO = + 5466
_______ _______
TRAIN 10932
Work done on paper. yay.
Note: Thank you Fiona for this week's POTW! <3
Maxwell's Grade 8 POTW:
ReplyDeleteThere were many different answer that could have fit in with the criteria. 5488 + 5488 = 10976 equation works. All my work and other answers are on my math notebook.
"other answerS". There are just 2 (pretty sure).
DeleteT=1 because a 4 digit number plus a 4 digit number can only be a 5 digit number starting with 1 or a 4 digit number. R seems likely to be 0 because it would not fit many other places.
ReplyDeleteCHOO
CHOO
10AIN
5HOO
5HOO
10AIN
54__
54__
109or8IN
Now it is just guess and check
5466
+5466
_____
10932 is one answer, but 5488+5488=10976 also works, and if I tried long enough, I know there are probably more answers.
"If I tried long enough". Trust me. You don't want to and there are not more I believe.
DeleteEsther POTW #10
ReplyDeleteTo make this true it must mean that:
C+C = TR
H+H = A
O+O = I
O+O = N
O's have to be the same, but have a different sum, meaning it must be over 5 to make the sum over 10.
I can choose 6, and get
_ _ 66 + _ _ 66 = _ _32
Now since no other numbers can be the same, 6, 3, and 2 cannot be any of the remaining letters.
The H's can be any number that has a sum less than 10, but the catch is that from 1, 2, 3, and 4, 2 and 3 are taken up. So the number must be 1 or 4. I can randomly choose 4 and get :
_ 466 + _ 466 = 932
For the the C's I just need a number that will be a two digit number when added. I can just choose 5 for example.
FINAL ANSWER:
CHOO = 5466
TRAIN = 10932
I got c=6 h=4 o=7 and t=12 r=9 a=5 n=4
ReplyDeleteI don't entirely understand that, but you used multiple values more than once as in 4
Deletewhere is the i in train? why is t two numbers?
DeleteFirst, I know that 2 x CHOO= TRAIN.
ReplyDeleteI know that O has to be greater than 5, because N and I are different numbers.
I also know that C has to be greater than 5, too. I will pretend that O is 6.
_ _ 66 + _ _ 66 = _ _ 32
That means that the rest of the numbers can not be 6, 3, or 2.
I will now pretend that H is 4.
_ 466 + _ 466 = _ 832
The rest of the numbers can not be 8 or 4 now.
Now, I will pretend that C is 5.
5466 + 5466 = 81032
C = 5
H = 4
O = 6
T = 8
R = 1
A = 0
I = 3
N = 2
I did guess and check and got the numbers: 5466 + 5466 = 10932.
ReplyDeleteC = 5
H = 4
O = 6
T = 1
R = 0
A = 9
I = 3
N = 2
Math on paper
ReplyDelete5488
+5488
------
10976
0=8
n=6
i=7
h=4
a=9
c=5
r=0
t=1
Grade 8 POTW
ReplyDeleteCHOO = 5488
5488
+5488
-----
10976
TRAIN = 10976
To solve this, I used guess and check and tried different combinations until I got one that worked.
POTW #10:
ReplyDeleteFrom the given information, we know that:
- O is a number higher than 4 because in the equation, the first two Os equal N but if we repeat the O again, It's a I. Therefore, something happened to the N to make it a I
- Each digit is a different letter. If they're the same, then they should have the same letter.
- C is higher than 4 because if it's doubled by itself it equals an extra digit in the answer.
Steps:
We know that TR has to be made out of an number doubled itself, over 4. So let's start with 5.
C = 5
So than we know that T is 1 but since we don't know the other digits yet, we won't decide what R is.
C = 5
T = 1
Now we should start with O because when you first add/subtract something, you start with the units digit.
We know that O has to be over 4. We can't make 5 O, because C is already 5 so, I'll use second lowest number over 4 besides 5, which is 6
5H66
+ 5H66
--------
1RAIN
So now we'll add the sixs together
5H66
+ 5H66
--------
1RA32
So we've used 1,2,3,5,6. For H, since it's the lowest number available, and if it's a low number, it can add up to a higher number and it (Letter/Number) won't be taken.
5466
+ 5466
--------
10932
And this combination works! So the answer is:
5466
+ 5466
--------
10932
CHOO
+ CHOO
--------
TRAIN
Although, I know or, I assume there are many different ways and answers to question, the answer I have, is this.
Ruby's Grade 7 POTW:
ReplyDeleteThe answer that I got was
5488
+ 5488
-------
10976
To solve this question I just did trial and error and guessed a bunch of combinations until I found one that worked.
For CHOO, I started with the number 5 and just kept guessing until I found the combination that worked, which is 5488. I multiplied that by two and got 10976.
The two answers that Fiona had provided that work are:
ReplyDelete5466+5466=10932
5488+5488=10976
Do you know of any others that fit the criteria and satisfy the question? Please see Fiona if you do.
Xie xie for the excellent Fi!!!!!!
Esther POTW #10
ReplyDeleteA 4 digit number multiplied by 2 = a 5 digit number with all different digits
The first thing I thought was that C has to be 5 or more in order to create a 5 digit number
O is the same number but it again, creates a 5 digit number, meaning those have to be over 5 as well, in order to equal to a 2 digit number.
I'll assume that C is 5, for sake of trial and error
that leaves the next number greater than 5 to be 6, what I can try out to be the Os.
So far I have
5_ 66
+5_ 66
=10132
However, in the sum, there are 2 ones. In TRAIN, all the numbers are different digits. I can do
5266 + 5266 = 10532
Which cannot work because 5 shows up in both TRAIN and CHOO
5366 + 5366 = 10732
Which is wrong again because of the same reason
5466 + 5466 = 10932
This works as the letters in TRAIN show up once in the entire equation, and the numbers fill out the criteria.
CHOO = 5466
TRAIN = 10932
5488+5488=10976
ReplyDeleteGrade 7 POTW:
ReplyDeleteWhat I'm going to do first is write down the given information.
- Rory eats 1/2 of the apple on the way there
- From there, he splits it in half again
- Rory ate twice the amount of apple as Edwyn later
It also tells me to find out the length of the bus ride, but figuring that out can come later. So first, I need to find out how much Rory gave Edwyn, as I already know that on the way there, Rory ate 50%, 0.50, or 1/2 of the apple.
It also mentions that Rory splits the already eaten apple in half, which would make a quarter. (1/4, 25%, 0.25) If he splits THIS in half as well, then that will be an eighth of the apple. So he gives an eighth of the apple to Edwyn, and then he eats twice the amount of apple as Edwyn does. As Edwyn eats one eighth, that means that Rory eats two eighths, or one quarter.
As it's starting to get a little bit complicated, I decided to write down exactly how much of the apple was missing, and the remainder of the apple that Rory would end up giving Mr Milette. (A very kind gift.)
As I know that he splits the apple and eats half of it at the very beginning, I know that only half of the apple is remaining. Then I also know that he gives an eighth of the apple to Edwyn and eats two eighths himself, so if we calculate this in eighths now, we know that seven eighths of the apple is now gone, leaving one eighth of the apple for Mr Milette.
So the answer to the first part of the question is that 1/8 (0.125, 12.5%) of the apple was given to Mr Milette.
Let's answer the second part of the question now. It explains how for the first QUARTERway there, he gets hungry and eats half of the apple. (Apples are delicious.) Then for the next eight kilometers, he continues splitting and eating the apple. As the first quarterway there would be 25% of the way, if there were 16 km in total, it would make sense as it would be 4/16, or 1/4. Thus, a quarterway there. (Bows)
Rory gave Mr. Milette 1/8 of an apple. In other words he gave him 12.5% of the apple. The ride was 16 km long.
ReplyDeleteWork on paper.
Grade 7 POTW
ReplyDeleteC=5
H=4
O=0
O=0
5466+5466= 10932
T=1
R=0
A=9
I=3
N=2