Is it that easy?

Number Theory Level 3

How many boxes are crossed by a diagonal in a rectangular table formed by 199 × 991 199 \times 991 small squares?

1189 500 199 1000 991 Cannot be determined 1010 1011

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Arulx Z by Arulx Z , 20, India

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2 solutions

Venkatachalam J
Jun 26, 2018

Number of squares traversed by the diagonal = Row + Column – HCF(Row,Column) = 199 + 991 - HCF(199,991)= 199+991-1=1189

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Ratul Pan
Nov 11, 2015

It is simple. The formula is add the no of rows and columns and subtract the H.C.F. of the rows and columns.
Therefore 199+991-1=1189

1 Helpful 0 Interesting 0 Brilliant 0 Confused

Can you prove the formula?

Arulx Z - 5 years, 6 months ago

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