Hop on over

Logic Level 3

Brilli the bug is constrained to move on a number line ranging [ − ∞ , ∞ ] [-\infty ,\infty ] . It starts at 0 and can go either left or right but moves in a way such that the i i th 's move it takes i i steps.

What is the minimum number of moves required to reach 32 on the number line.

Details and Assumptions :

  • As an explicit example to reach position 3 3 it takes a minimum of 2 2 moves 0 → 1 → 3 0\rightarrow 1 \rightarrow 3

  • The i i -th move can be done with as a combination of left and right movement


The answer is 8.

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Beakal Tiliksew by Beakal Tiliksew , 24, Ethiopia

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3 solutions

32 = 1 − 2 + 3 + 4 + 5 + 6 + 7 + 8 32=1-2+3+4+5+6+7+8

5 Helpful 0 Interesting 0 Brilliant 0 Confused

I did it manually too. Brute Forcing would be too tedious.

Arulx Z - 5 years, 10 months ago
Francis Naldo
Sep 5, 2015

First, assume that the bug is always travelling to the right until it reaches or surpasses 32. 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 = 36 which is 4 steps above 32..

Note: Whenever you change the direction of the bug from (+) to (-), the total distance of the bug will move to the left by twice of that number.

36 − 32 2 \frac{36 - 32}{2} = 4 2 \frac{4}{2} = 2 Therefore 32 = 1 - 2 + 3 + 4 + 5 + 6 + 7 + 8..

Answer = 8 \boxed{8}

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Rahul Saha
Dec 24, 2015

0+1+3+... From this the difference between 1&0 is 1, 3&1 is 2 So the difference are 1,2,3,4,5 0+1+3+6+10+15 From here 3th is 3 1=3,then 3 2=6, So we tell 3*8=24;

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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