there are 7 truck and 40 drum we want to put 40 drum in 7 truck in odd number
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40 drums has to be placed in 7 trucks.
Which means answer needs expressing 40 as sum of 7 odd no.s, which is impossible.
Due to the fact that odd no. multiplied by odd always gives odd
i.e., odd*odd= odd
7*(odd no. of drums in truck)= [odd]
but there are 40 drums, which is even
so,It is impossible.
===========<<<>>>============
proof for odd*odd= odd:
Consider 2 odd no.s
say (2m+ 1) and (2n+1)
(2m+1)(2n+1)= 4mn+2+2m+2n
= 2(mn+m+1)+1
= 2(K)+ 1
which is odd
It is also valid when m=n
i.e., when 2 same odd no. are considered.
;)
Hope it helps
Comment if you need to clear something ...
Which means answer needs expressing 40 as sum of 7 odd no.s, which is impossible.
Due to the fact that odd no. multiplied by odd always gives odd
i.e., odd*odd= odd
7*(odd no. of drums in truck)= [odd]
but there are 40 drums, which is even
so,It is impossible.
===========<<<>>>============
proof for odd*odd= odd:
Consider 2 odd no.s
say (2m+ 1) and (2n+1)
(2m+1)(2n+1)= 4mn+2+2m+2n
= 2(mn+m+1)+1
= 2(K)+ 1
which is odd
It is also valid when m=n
i.e., when 2 same odd no. are considered.
;)
Hope it helps
Comment if you need to clear something ...
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