Conversation Logic
The following is a conversation between Cheryl, Albert and Bernard. Cheryl: I thought of 2 distinct one-digit numbers. Can you guess the sum of these two numbers? Albert and Bernard: No. Can you give us a clue? Cheryl: The last digit of the product of the two numbers is the last digit of Albert's house number. Albert: Now I know what the sum of the 2 numbers is. Bernard: Although I don't know what Albert's house number is, I also know what the sum of the 2 numbers is.
What is the sum of the 2 numbers?
The answer is 10.
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1 solution
Let last digit of Albert house number be 2 . Then Albert concluded product of two number must end in 2 . The product can be 2 or 1 2 or 3 2 or 4 2 or 7 2 . So he cannot find the sum of that two numbers.
If last digit of Albert's house number is 3 . Then Albert concluded product of two number must end in 3 . The product can be 3 or 6 3 . So he cannot find the sum of that two numbers.
If last digit of Albert's house number is 4 . Then Albert concluded product of two number must end in 4 . The product can be 4 or 1 4 or 2 4 or 5 4 . So he cannot find the sum of that two numbers.
If last digit of Albert's house number is 5 . Then Albert concluded product of two number must end in 5 . The product can be 5 or 1 5 or 3 5 or 4 5 . So he cannot find the sum of that two numbers.
If last digit of Albert's house number is 6 . Then Albert concluded product of two number must end in 6 . The product can be 6 or 1 6 or 3 6 or 5 6 . So he cannot find the sum of that two numbers.
If last digit of Albert's house number is 7 . Then Albert concluded product of two number must end in 7 . The product can be 7 or 2 7 . So he cannot find the sum of that two numbers.
If last digit of Albert's house number is 8 . Then Albert concluded product of two number must end in 8 . The product can be 8 or 1 8 or 2 8 or 4 8 . So he cannot find the sum of that two numbers.
If last digit of Albert's house number is 9 . Then Albert concluded product of two number must end in 9 . The product can be 9 . Only one possible product which occurs when two numbers are 9 and 1 . So its sum is 1 0 .
If last digit of Albert's house number is 0 . Then Albert concluded product of two number must end in 0 . The product can 1 0 or 2 0 or 3 0 or 4 0 . So he cannot find the sum of that two numbers.
At last, if last digit of Albert's house number is 1 . Then Albert concluded product of two number must end in 1 . The product can be 2 1 . Only one possible product which occurs when two numbers are 7 and 3 . So its sum is 1 0 .
Since in both the case, sum is same. This is the only reason why Bernard also know the sum of two numbers. Albert know exactly what are that two numbers but Bernard only know the sum. The sum is 1 0 .