## Solution to Puzzle #82: Guess the Number

I got many correct answers for this puzzle. The first one to send the correct answer was Sandeep Verma from California. I also got correct answers from my niece Radhika, and from Girish Tutakne and Anubhav Garg.

I am reproducing the answer from Sandeep Verma, which is only slightly different than the one I am posting on video (BTW, LSD means Least Significant Digit and MSD means Most Significant Digit):

EFGH

X 4

——–

HGFE

Since multiplication of 4 and E in the MSD doesn’t lead to  carry over, E has to be either 1 or 2

Since LSD H*4 is E, E can not be 1. So, E=2

This implies H is either 3, or 8, since H*4 ends in E=2 being the units place. From the MSD, H of the result we know that H>4, so H=8

Now from middle two digits,

(G*4+3) mod 10 = F

LHS has to be odd, hence F is odd.

4*F+Carryover from above=G. Since there is no carryover to the MSD, E (4*2=8),

4*F+CO <= 9. Only values of 1 and 2 can satisfy this inequality for F.

As F has to be odd, F=1

Going back, G*4 + 3 = 11 V 21 V 31. G*4 ends in 8 in the units place. This means G=2 or 7. G*4+3 will be 11 or 31 respectively

For G=2, 4*(F=1)+1=2 is incorrect

For G=7, 4*(F=1)+3=7 is correct; hence G=7

Putting together, EFGH=2178 and HGFE=8712.

Moment of truth, 2178*4=8712

Here is a link to a video that explains the answer as well, which might be easier for children:

Hope you enjoyed the puzzle!

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