Hello, DISCLAIMER: I am not trying to get my homework done. This quiz is provided as it is, and I do have the answer. So it is a challenge for anyone. Best answer will be awarded in approximatively one day. Have fun gals and guys!
= = = = = = = = John and Bob are chatting on the first days of 2016:
John: What about your daughter Mary's birthday this year? What about a nice doll? Bob: That would not be appropriate. Must I remind you that her age this year will be the sum of the digits of her year of birth? John: Sorry, I'll think of something else.
► Mary, being an human being, has a life expectancy of approximatively 100 years. So she is either born in this century (20AB) or the previous one (19AB).
► Considering this century: 2 + 0 + A + B = 2016 – (2000 + 10A + B) 2 + A + B = 16 – 10A – B 11A + 2B = 14
Now 14 is even, and obviously 2B too. So 11A must also be even, implying the digit A must be even: A in { 0; 2; 4; 6; 8 } Since any A greater than 1 would make B negative, the only possibility is A = 0 Leading to B = 7 With a birth year of 2007 and age of 9 in 2016.
► Considering the previous century: 1 + 9 + A + B = 2016 – (1900 + 10A + B) 10 + A + B = 116 – 10A – B 11A + 2B = 106
Now 106 is even, and obviously 2B too. So 11A must also be even, implying the digit A must be even: A in { 0; 2; 4; 6; 8 } If A=8 → 11A=88 and 106–88=18 → B=9 If A=6 → 11A=66 and 106–66=40 → B=20 ◄Impossible B is a digit If A=4 → 11A=44 and 106–44=62 → B=31 ◄Impossible B is a digit ...and decreasing A will only increase B, leading to non-digit values of B.
So the only possibility is A = 8 and B=9 With a birth year of 1989 and age of 27 in 2016.
► Lastly you are told it is inappropriate to gift Mary a doll. Now you have to ask yourself: "Is 9 years of age too old for a doll?" Well, I don't know, but 27 certainly is, unless Mary is into collectable dolls, which we can assume to the contrary.
Thus the expected answer was 1989, reachable with basic maths and common sense.