The sum 1+2+3+....n is equal to one three-digit number with the same digits. Determine that number.
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In 5 seconds you can solve the equation
2
n(n+1)
=aaa (111, 222, etc)
2
n(n+1)
=aaa=a×111=a×3×37 ⇒n(n+1)=6ax37
The L.H.S of the equation n(n + 1) is a product of two consecutive
natural numbers Therefore R.H.S. should also be a product of two
consecutive natural numbers One of the numbers is 37 Therefore the other number, 6a consecutive to 37 can only be 36 giving a = 6 and n = 36
Therefore 36 numbers have been summed up and their sum
is equal to 666
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