Summer of Code/Sanjay Kumar: Difference between revisions
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<code> | <code> | ||
Challenge your friend to answer (999989) | Challenge your friend to answer (999989)^2 | ||
2 | |||
in 10 seconds ;) | in 10 seconds ;) | ||
Its simply: Question - 11 | 000 | (11) | Its simply: Question - 11 | 000 | (11)^2 = 999978000121. | ||
2 = 999978000121. | |||
</code> | </code> | ||
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<code> | <code> | ||
Trick 02 : Square of numbers just below 100 | Trick 02 : Square of numbers just below 100 | ||
Let us find (x) | Let us find (x)^2. X is just below 100. | ||
2 | |||
. X is just below 100. | |||
Step 01: Find the difference between 100 and this number. | Step 01: Find the difference between 100 and this number. | ||
Step 02: Now, Subtract the difference from the number (x). | Step 02: Now, Subtract the difference from the number (x). | ||
Step 03: Find x | Step 03: Find x^2 | ||
2 | |||
Answer = Step 02 | Step 03 | Answer = Step 02 | Step 03 | ||
Example: | Example: | ||
Question: (96) | Question: (96)^2 | ||
2 | |||
Step 01: Difference is 4 (100 - 96 = 4) | Step 01: Difference is 4 (100 - 96 = 4) | ||
Step 02: 96 - 4 = 92 | Step 02: 96 - 4 = 92 | ||
Step 03: (4) | Step 03: (4)^2 = 16 | ||
2 = 16 | |||
Answer = 9216 | Answer = 9216 | ||
</code> | </code> | ||
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<code> | <code> | ||
Trick 03 : Square of numbers just above 100 | Trick 03 : Square of numbers just above 100 | ||
Let us find (Y) | Let us find (Y)^2. Y is just above 100. | ||
2 | |||
. Y is just above 100. | |||
Step 01: Find the difference between the number and 100. | Step 01: Find the difference between the number and 100. | ||
Step 02: Now, Add the difference to the number (y). | Step 02: Now, Add the difference to the number (y). | ||
Step 03: Find y | Step 03: Find y^2. Add | ||
2 | |||
. Add | |||
Answer = Step 02 | Step 03 | Answer = Step 02 | Step 03 | ||
Example: | Example: | ||
Question: (104) | Question: (104)^2 | ||
2 | |||
Step 01: Difference is 4 (104 - 100 = 4) | Step 01: Difference is 4 (104 - 100 = 4) | ||
Step 02: 104 + 4 = 108 | Step 02: 104 + 4 = 108 | ||
Step 03: (4) | Step 03: (4)^2 = 16 | ||
2 = 16 | |||
Answer = 10816 | Answer = 10816 | ||
</code> | </code> | ||
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<code> | <code> | ||
Trick 04 : Square of any three digit ending with zero in between | Trick 04 : Square of any three digit ending with zero in between | ||
Let us find (x0y) | Let us find (x0y)^2. Digits are referred from left to right. | ||
2 | Step 01: Square third digit (y)^2 | ||
. Digits are referred from left to right. | |||
Step 01: Square third digit (y) | |||
2 | |||
Step 02: Multiply x with y and double the answer ( x * y * 2 ). The answer is of two | Step 02: Multiply x with y and double the answer ( x * y * 2 ). The answer is of two | ||
digits. Add zero in front, if it is in single digit. | digits. Add zero in front, if it is in single digit. | ||
Step 03: Square first digit (x) | Step 03: Square first digit (x)^2 | ||
2 | Answer = Step 03 | Step 02 | Step 01 = (x)^2 | ( x * y * 2 ) | (y)^2 | ||
Answer = Step 03 | Step 02 | Step 01 = (x) | |||
2 | |||
| ( x * y * 2 ) | (y) | |||
2 | |||
Example: | Example: | ||
Question: (504) | Question: (504)^2 | ||
2 | |||
Step 01: (4) | Step 01: (4)^2 = 16 | ||
2 = 16 | |||
Step 02: 5 * 4 * 2 = 40 | Step 02: 5 * 4 * 2 = 40 | ||
Step 03: (5) | Step 03: (5)^2 = 25 | ||
2 = 25 | |||
Answer = 254016 | Answer = 254016 | ||