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I have tied my square bathroom wall with congruent square tiles. All the tiles are red, except those along the two diagonals, which are all blue. If `

Monjur Alahi

I have tied my square bathroom wall with congruent square tiles. All the tiles are red, except those along the two diagonals, which are all blue. If `I` used `121` blue tiles, then the number of red tiles `I` used are
A. `900`
B. `1800`
C. `3600`
D. `7200`


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Salim Ahmed Kawsar

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Correct Answer - A
`(a)` Let the square has dimensions `nxxn`.
If `n` is even, total no. of blue (diagonal) tiles `=n+n=2n`
If `n` is odd, then total no. of blue tiles `=n+n-1=2n-1`
(the middle tile is be counted twice).
Hence, `2n-1=121impliesn=61`
So, number of red tiles `=61xx61-121=3600`

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