A problem by Yuvraj 007
Level
pending
Three different non-zero digits are used to form six different 3-digit numbers. The sum of five of them is 3231. What is the sixth number?
The answer is 765.
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1 solution
first get an average of the sum so that you can get an idea about required digits.
The average(divide the sum by 5) comes around 646.2 that means if you take digits like 1,2 or 3 you not likely to get the sum of those five of them near to 3231. so start from bottom.
suppose X,Y,Z are three digits.Then your numbers will be XYZ ,XZY, YXZ, YZX, ZXY and ZYX
suppose X=9 Y=8 Z=7 If you put the values above you'll see the sum is bigger than 3231. To make it quick,you just add 2 900, 2 800 and 1*700 .You see it's more than our need. so then try 6,7 and 8 which will also produce a bigger sum
then you take 5,6 and 7 put the values above and add five numbers .
If the sum is equal to 3231, then you get the answer by reordering the digits which was multiplied by 1.
you will get your answer if not at the first time but in the second try for sure.