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SNGLOOP1 - Easiest Loop 1 |
Ileana D'Cruz is taking programming classes but she is having problem in understanding while loops. She is working on following set of instructions -
INTEGER I = 0, S, U = 1010;
WHILE (I < U) {
S = (3 * S) + (5 * I);
I = I + 1;
}
Let Sk be the value assigned to INTEGER S for the iteration I = (k + 1) and n, m, p be positive integers such that m > n. Ileana knows the values of n and m but she forgot the initial value of S. She is trying to find the unit digit of p. Any initial value of S may be used. She also knows the following equality -
(2 * n + 3) * (p - 1) + (4 / 5) * [(p * Sn) - Sm] = 2 * (m - n)
Input
First line of input is T (total number of test cases). Each of next T lines contains two integers n and m.
Output
Print unit digit of p (p % 10) for each test case in separated lines.
Example
Input: 1 2 3 Output: 3
Constraints
T < 10001
Explanation
Let S = 2
S0 = 6
S1 = 23
S2 = 79
S3 = 252
Now solving the equation gives p = 3.
Added by: | AvmnuSng |
Date: | 2014-06-14 |
Time limit: | 1s |
Source limit: | 50000B |
Memory limit: | 1536MB |
Cluster: | Cube (Intel G860) |
Languages: | All |
Resource: | Abhimanyu Singh My Problems |
hide comments
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2019-01-08 19:02:36
getting back to the very basic concept of physics's derivations, finally got me an AC! Pheww Last edit: 2019-01-08 19:26:38 |
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2016-02-27 13:25:54
took my 3 hours! AC @ping_of_death: :...खोदा पहाड़ निकली चुहिया...: agree_with_U |
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2016-01-01 19:17:13 KD
Damn easy but it makes my century :) Last edit: 2016-01-01 19:17:35 |
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2015-01-09 13:19:16 Saksham
a very good indeed |
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2014-12-15 10:15:38 bourne
I think @Rahul Jain is correct. Not satisfying for S=0. Although the proof is easy for other values of S. Ignore the pattern and Try it :) ! |
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2014-12-15 07:28:22 Vamsi Krishna Avula
I was not able to prove it mathematically but observing the pattern was easy enough. |
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2014-10-24 13:36:16 ping_of_death
one of the best problem....this is like ....खोदा पहाड़ निकली चुहिया...:P |
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2014-09-28 21:17:42 Rahul Jain
Take initial S=0 or 1, the sample test case is not satisfying. |
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2014-07-28 23:46:00 VenkateshP
My O(1) algo giving TLE in Java @Abhimanyu can you look at my submission 12041122? Reply: Use fast IO in Java... Last edit: 2014-09-01 00:06:22 |
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2014-07-02 23:44:43 aqfaridi
@Quantum : no pattern involved , just solve the given equation manually.. thats it :) |