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.
hide comments
prabhav_123:
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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mcjoshi:
2016-02-27 13:25:54
took my 3 hours! AC
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KD :
2016-01-01 19:17:13
Damn easy
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Siddharth Singh:
2015-12-26 12:49:34
Interesting One , the given explanation Helped me device a trial an error formula which to my surprise worked :D
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मोहन:
2015-02-06 11:51:34
Here comes a my 100th!!! :) |
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Saksham :
2015-01-09 13:19:16
a very good indeed
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bourne:
2014-12-15 10:15:38
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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Vamsi Krishna Avula:
2014-12-15 07:28:22
I was not able to prove it mathematically but observing the pattern was easy enough. |
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NEXES:
2014-11-29 18:42:26
AC in one go.....
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ping_of_death:
2014-10-24 13:36:16
one of the best problem....this is like ....खोदा पहाड़ निकली चुहिया...:P |
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 |