Question

using digits 1-9 . Make 3 number of 3 digits using each digit only once so that 2 number is double of 1. and 3 number is triple of 1 number

Answer 1

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Which 3 three-digit numbers created using 1-9 when added give a sum of 1000? (_ _ _ + _ _ _ + _ _ _ ) = 1000?
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The total sum of all the digits used will be 9*10/2 = 45.

Now to create 1000, at all places (unit, tens, hundred) you should get either 20 or 10 and at hundred you should get 10 (including carries).

So the sum of digits at hundred place should be 9/8 as it will use a carry from tens place (which will be definitely created to get 0 at tens place). So we remain with sum of 36/37. So there are two case unit places gives 20 or 10.

Case A : Unit Place -> 20 :

But if we get 20 from unit place, we should get 18 from tens place and carry will make it 20 or we should get 8 and carry will make it 10. In both cases it not possible.
Case 1: Unit Place -> 20, Tens place -> 8, Hundred Place -> 9, Total sum of digits = 37 not possible. (As it should be 36)
Case 2: Unit Place -> 20, Tens Place -> 18, Hundred Place -> 8, Total sum of digits = 46 not possible. (As it should be 37)

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