The Case of the Missing Digit
A friend of mine asked me to write down any multidigit number.
But, he put a condition, the number should not end with a zero.
I put down the number 96452
Then he asked me to add up the five digits and subtract the total
from the original number.
I did and here is what I got :
96452 – 26 = 96426
He then asked me to cross out any one of the five digits and tell him
the remaining numbers. I crossed out the 2 and told him the rest of
the digits. I neither told him the original number nor what I had
done with it. Yet ‘pop’ he told me the exact number I had crossed
out.
How do you explain it ?
pls i need fast pls pls pls
Answers
Given : write down 5 digit number. add up the five digits and subtract the total . cross out any one of the five digits and tell him the remaining numbers from the original number.
To find : Missing Digit / Cross out Digit
Solution:
Let say 5 Digit number = ABCDE
Value =10000A + 1000B + 100C + 10D + E
Sum of Digits = A + B + C + D + E
Number after Subtracting sum of Digits
Digit = 10000A + 1000B + 100C + 10D + E - (A + B + C + D + E)
= 9999A + 999B + 99C + 9 D
= 9(1111A + 111B + 11C + D)
Resultant number is Divisible by 9
a number is Divisible by 9 if Sum of Digits is Divisible by 9
Person told him Digits 9 , 6 , 4 & 6 and missing Digit = X
Sum = 9 + 6 + 4 + 6 + X
= 25 + X
25 + X should be divisible by 9
hence X = 2
So he was able to tell the number you crossed
Learn more:
Find the missing digit, if the number 7254*98 is divisible by 22.995 + ...
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