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Hi Stephen,
Where you draw the line will depend on the number of digits in the flag. If the flag has one digit, then you will draw the decimal line after one digit from the right.
In your example 1 is the pole and 3 is the flag. The flag is a one digit number which is 3. So you will draw the line between 2 and 4 in 64924 (i.e 6492|4).
If you divide 64924 by 224 then where you draw the line will depend on how you create the flag and the pole.
If in 224 you make 22 the pole and 4 the flag, then you will draw the line between 2 and 4 in 64924 (i.e 6492|4) because the flag 4 is only one digit.
If in 224 you make 2 the pole and 24 the flag, then you will draw the line between 9 and 2 in 64924 (i.e 649|24) because the flag 24 is two digits.
Hope this clarifies.
Here are the steps
125 x 8 = _ _ _ _
Multiplying Left to Right one digit at a time
We multiply 1 x 8 to get 8 which becomes the first digit of the answer.
125 x 8 = 8 _ _ _
We multiply 2 x 8 to get 16. We carry over the 1 in 16 so 8 becomes 9.
125 x 8 = 9 _ _ _
The second digit of 6 becomes the next digit of the answer.
125 x 8 = 9 6 _ _
We multiply 5 x 8 to get 40. We carry over the 4 in 40 so 96 becomes 100.
125 x 8 = 1 0 0 _
The 0 in 40 becomes the next digit of the answer.
125 x 8 = 1 0 0 0
1000 is the final answer.
Hi Akiva,
The denominator in your code does not include cases where the DS method correctly predicts a calculation as incorrect.
I have updated your code to reflect this and you can find the notebook here: https://github.com/abhivr/public_repo/blob/main/Digit_Sum_Checker.ipynb
When I wrote the book & created the course, I estimated the accuracy of the DS method using simple probability.
The digit sum can only be a number between 1 to 9. So there are 9 possible values.
8 of these 9 possible DS values will help you catch an error in the calculation without an issue.
One out of these 9 possible values is the DS of the correct answer but it can also be the DS of the incorrect answer.
So there are actually a total of 10 possible values for the Digit sum (9 Correct DS + 1 Incorrect DS) with one number repeating in Correct DS and Incorrect DS.
So 9 / 10 (90%) the DS method correctly predicts the calculation as incorrect & correct. But 1/10 times the DS method predicts the calculation is correct when it is actually incorrect.
Hope this clarifies.
Hi Pradnesh,
You can use the Math Palace technique. It is still a work in progress. You can get a free review copy for leaving an review on Amazon.
Here is the link: https://ofpad.com/math-palace
Abhishek
Here are the steps:
We are trying to multiply
= 67 x 8.
We break down 67 into (70 – 3). So we get:
= (70 – 3) x 8
Multiplying the individual numbers we have.
= 560 – 24
LR Subtraction without Round Up.
Here we subtract left to right.
560 – 24 = _ _ _
First number is 5 so it becomes the first digit of the answer.
560 – 24 = 5 _ _
Second digits is 6 – 2 = 4 it becomes the second digit of the answer.
560 – 24 = 5 4 _
We cannot subtract 0 – 4 so we must borrow 1 from the existing answer 54 so it becomes 53.
560 – 24 = 53 _
Now we subtract 10 – 4 to get 6 which is the last digit of the answer.
560 – 24 = 536.
Alternative LR Subtraction with Round Up.
If you want to do the LR Subtraction with round up, then here are the steps. To recap we are trying to subtract
560 – 24 = _ _ _
We can round up 24 to 30 so the equation becomes:
560 – (30 – 6) = _ _ _
530 – 30 + 6 = _ _ _
We subtract 560 – 30 to get 530
560 – 30 = 530.
We add the amount we rounded up which is 6 to get 536.
530 + 6 = 536.
536 is the final answer for 67 x 8.
Hope this clarifies.
Hi
You need to carry over the 1 in 11 in your answer.
Here are the steps:
736 + 255 = _ _ _
Adding 7 +2 we get 9. So 9 becomes the first digit of the answer.
736 + 255 = 9 _ _
Adding 3 +5 we get 8. And 8 becomes the first digit of the answer.
736 + 255 = 9 8 _
Adding 6 +5 we get 11. Since 11 has two digits, we carry over the first 1 in 11. So the answer 98 becomes 99.
736 + 255 = 9 9 _
The second 1 in 11 becomes the third digit of the answer.
736 + 255 = 9 9 1
Hope this clarifies.
You must alternate between odd and even.
For example let’s take
9876.1234
Odd is marked as O.
Even is marked as E.
9 8 7 6 . 1 2 3 4
E O E O . E O E O
You start alternating from the left of the decimal place which is odd.
Hope this clarifies
To check 8396 x 11 = 92356 using the DD Method
Here are the steps:
DD of 8396 is:
= Odd Digits – Even Digits
= (6+3) – (9 + 8)
= 9 – 17 = -8
If DD is negative we must add +11 so
= -8 + 11 = 3
DD of 11 is 0 (1 -1)
DD of 92356 is:
= (6+3+9) – (5 + 2)
= 18 – 7
= 11
11 is a two digit number. So we calculate the digit difference of that again and we get 0.
So the calculation is correct
3 x 0 = 0
Hope this clarifies.
Yeah the Math Palace method might seem challenging at first but this is the same method being used by Memory Champions to remember 1000+ digit numbers in record time.If you are rounding up and calculating you can use 4 or 5 memory palaces if you want. You can use two additional memory palaces one for the rounded up number and another for the amount you rounded up by. But usually you can just remember the rounded up number without any memory palace and you don’t have to remember the original number you rounded up to do the calculation.Let us take the example 503,401 – 398,972 = ???We can round up 398,972 to 400,000. Amount rounded up is 1028.You don’t have to use the number 398,972 again in your calculation so you don’t have to use a math palace to remember 398,972.The new calculation is 503,401 – 400,000 + 1028.You use a math palace just to remember 503,401 and 1028 as they are the main numbers in the calculation.Hope this answers your question.Welcome to the community John.
Feel free to post your questions in this community as you work your way through the book.
Hi C,
I prepared for case study interviews myself. Originally I was trying to get into Management Consulting (McKinsey, Bain), then somehow I got into analytics which also required the use of case studies.
I would suggest you post this question in Management Consulting Facebook groups. You will surely find someone there.
Hi Mathew,
Did your ISP list any reason for the block? I will try to resolve it from my end.
Sorry for the late reply. I was on vacation but looks like you figured it out.
The method in the book is just to round up to the nearest multiple of 10, 100 or 1000.
In your question 5492 = 8000 – ____, the nearest multiple of 5492 is actually 6000 not 8000.
So 5492 = 6000 – 508.
If you want to round up to the next multiple of 1000 which is 7000 then you add 1000 to 508 to get 1508.
If you want to round up to 8000 then you need to add 2 x 1000 = 2000.
You can subtract the first digit of both numbers and then subtract the difference by one.
In 5492 = 8000 – _____
8 – 5 – 1 = 2
9 – 4 = 5
9 – 9 = 0
10 – 2 = 8
So the rounded up number is 2508
5492 = 8000 – 2508
Hope this provides more clarity.
Welcome to the community.
Hope you and your family are safe during these difficult times.
Are you transitioning to online teaching? You will find that you can make a bigger impact for the same effort when you harness technology and teach online.
When are you getting yourself a golden retriever? ?
Just be careful about how you approach that one Yassine.
Waking up early not really a habit itself. It is actually the outcome of other good habits like going to bed at the same time everyday and getting enough sleep.