Question

*puzzle: there are different number of pairs of socks of different colors c1 c2 c3 ???. c20 such that there is 1 pair of c1 2 pairs of c2 3 pairs of c3 ???. 20 pairs of c20. what is the maximum number of socks you need to take out such that a pair is made containing both the pieces of same color.

Answer 1

Solution:  Maximum number of socks such that a pair is made containing both the pieces of same color = 420.

Explanation:

Given: number of pairs of socks of color c1 = 1

number of pair of socks of color c2 = 2

number of pairs of socks of color c3 = 3

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.

.

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and number of pairs of socks of color c20 = 20

then the total number of pair of socks = $1+2+3+4+5+...+20$

we know that ∑n= $\frac{n\times \left ( n+1 \right )}{2}$

so,by using this formula, total number of pairs of socks = $\frac{20\times \left ( 20+1 \right )}{2}$ = 210

So the maximum no. of pair of socks such that the pair is made containing both the pieces of same color = 210

As we know that a pair contains 2 socks. So, max.  number of socks such that a pair is made containing both the pieces of same color = 2×210 = 420