Solution to Puzzle #49: The Absent Minded Bank Clerk

I surprisingly got much fewer responses than I expected, and in hindsight, the “two minute” qualifier probably scared people! Congratulations to Muskaan Mittal, a brilliant 9 year old, in being the first one to send the answer. Girish Tutakne and Ashish Gupta were the other ones.

The source (Martin Gardner) uses algebra to solve the puzzle. Clearly one can do that. Solution that I am presenting here does not use algebra, but requires a bit of trial and error along with some logic. Here is how it goes:

– Assume that the number is D.C (Dollar and Cents)

– Bank Clerk gave him C.D

– After the newspaper, he has C.D-5 (assuming there is no carryover)

On the way to the solution, following conclusions can be drawn:

#1: D is an odd number (after you subtract 5, it needs to be even as the number left is twice of the original check amount)

#2: C >=50 and D >= 25 (if this is not the case, then C needs to be exactly twice of D and D needs to be almost twice of C, actually a little more i.e. by 5 additional cents, both of which are not possible)

#3: D < 50 otherwise C will need to be more than 100, which is not possible since cents in a check need to be max 99

#4: Therefore, when one doubles D.C, there will be a carry over, and that means that C is also an odd number because of the carry over.

#5: The number, therefore, needs to be of the form D.2D+1

Beyond this, a little bit of trial and error leads to $31 and 63 cents which is the only answer.

Hope you enjoyed the puzzle!

 

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