Tessellate S.T.E.M.S - Computer Science - School - Set 1 - Problem 3
The value of a function is defined using the following rules (if multiple rules apply, then the one at the top of this list is applied)
- If ,
- If ,
- If ,
- Otherwise,
What is the value of ?
This problem is a part of Tessellate S.T.E.M.S.
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f(1,1,1)=1+f(1,1,2)=1+(1+f(1,1,3))=......=10+f(1,1,11)
f(1,1,11)=f(1,2,1) by cond. 3
Again, f(1,2,1)=1+f(1,2,2)=1+1+f(1,2,3)=......=10+f(1,2,11)
Once again by cond. 3, f(1,2,11)=f(1,3,1)
Thus for every i and j, k goes from 1 to 10, adding 1 to the output. Thus, for every i,j, value increases by 10. Observe that similarly, j goes from 1 to 10, before i increases. Thus, the function can be seen as loop as follows:
s=0;
for(i=1;i<=10;i=i+1){
for(j=1;j<=10;j=j+1){
for(k=1;k<=10;k=k+1){
s=s+1;
}
}
}
So i-loop runs 10 times, j-loop runs 10 times each for every value of i, and k-loop runs 10 times each for every value of j. Thus in total, s increases by 10* 10* 10=1000