27. What's my height and weight? ;)
hint: just make the answer flattering. I of course would reply, "That's right!," and everyone will think you have a really neat trick.
27. What's my height and weight? ;)
hint: just make the answer flattering. I of course would reply, "That's right!," and everyone will think you have a really neat trick.
That was cool. Got the proof. Thanks. Gleaned it while it was here temporarily. Learn something new every day.
Here's how I did it
33333 is my number they add to 15. 33333-15=33318. Say I cross an 8. I add up 3,3,3, and 1, which is 10. 18 is one of the multiples of nine, and its a number closest to, but greater than 10. 18-10= 8
12345 = 1*(9999+1)+2*(999+1)+3*(99+1)+4*(9+1)+5*(0+1) = 1*9999+2*999+3*99+4*9+5*0 + 1+2+3+4+5 = 9*(1*1111+2*111+3*11+4*1+5*0) + 1+2+3+4+5
Every number minus the sum of its digits is a multiple of nine. Similarly, every multiple of nine has the sum of its digits a multiple of nine. Now, crossing out a digit and then summing is identical to summing and then subtracting the digit. Therefore, the only non-zero digit such that the answer sums to a multiple of nine is the digit crossed.
12345 = 1*(9999+1)+2*(999+1)+3*(99+1)+4*(9+1)+5*(0+1) = 1*9999+2*999+3*99+4*9+5*0 + 1+2+3+4+5 = 9*(1*1111+2*111+3*11+4*1+5*0) + 1+2+3+4+5
Every number minus the sum of its digits is a multiple of nine. Similarly, every multiple of nine has the sum of its digits a multiple of nine. Now, crossing out a digit and then summing is identical to summing and then subtracting the digit. Therefore, the only non-zero digit such that the answer sums to a multiple of nine is the digit crossed.
nice work :)
Dear Einstein
,
Don’t forget the advise on NOT finding out our weight. And before I forget, we’re sensitive on the age thing too…well, not all of us – only those that surpass a certain age.
Yours Sincerely,
Ally