The census taker says, "I need to know the ages of your children."
The mother replies, "I have no one-year-olds. The product of my
children's ages is 90, and the sum of their ages is the same as my
house number."
The census taker replies. "I can see the house number but I still need
more information."
The mother says, "You're right. You also need to know that the boy
across the street is older than my oldest child."
The census taker says, "Thank you, I now know the ages of your
children."
What are the ages of the children?
What is the house number?
What is the age of the boy across the street?
I made a list of factors, but don't know where to go from there. Thank you for your help!
Can you post the list of factors that you have made?
I feel like I'm missing information, but here's the best I can do.
Product of ages = 90
Prime factors of 90: 2,3,3,5
So the possible number and age of children are:
2,3,3(twins),5
3,5,6
2,5,9
3,3(twins),10
2,3,15
6,15
5,18
Since the mother said "...older than my oldest child.", there must be three or more children, or even three different ages. That leaves us with:
2,3,3(twins),5
3,5,6
2,5,9
2,3,15
Some cities do not put 13 as a house number, so we eliminate the first case, to leave us with:
3,5,6 (sum=14)
2,5,9 (sum=16)
2,3,15 (sum=20)
If we eliminate ages that are too close, one year apart (but logically & physically feasible), that leaves us only with 2,5,9 (sum=16).
Also, the boy across the street can be one or more years older than the oldest child.
If you have other hints/conclusions, please post.
To solve this puzzle, let's go step by step and use some logical deduction.
First, let's list out the possible combinations of three numbers whose product is 90.
1, 1, 90
1, 2, 45
1, 3, 30
1, 5, 18
1, 6, 15
2, 3, 15
2, 5, 9
3, 3, 10
3, 5, 6
Now, let's consider the statement that the sum of their ages is the same as the house number. We don't know the house number yet, but we can look at the possible sums and see if there is any combination where two sums are the same.
For example, if the house number is 45, we can see that the sum of the ages in the second combination (1, 2, 45) is 48, which is not equal to the sum of ages in any other combination.
Next, let's consider the statement that the boy across the street is older than the oldest child. This gives us some additional information. Since the census taker claims to have figured out the ages of the children after hearing this information, it means that there must be only one possible combination of ages where the boy across the street is older than the oldest child.
Now, let's consider each possible combination while considering the age of the boy across the street:
1. In the first combination (1, 1, 90), both children are the same age, so this is not possible.
2. In the second combination (1, 2, 45), the boy across the street must be older than 2. If the boy were 1, it would contradict the statement.
3. In the third combination (1, 3, 30), the boy across the street must be older than 3. If the boy were 1 or 2, it would contradict the statement.
4. In the fourth combination (1, 5, 18), the boy across the street must be older than 5. If the boy were 1, 2, 3, or 4, it would contradict the statement.
5. In the fifth combination (1, 6, 15), the boy across the street must be older than 6. If the boy were 1, 2, 3, 4, or 5, it would contradict the statement.
6. In the sixth combination (2, 3, 15), the boy across the street must be older than 3. If the boy were 1 or 2, it would contradict the statement.
7. In the seventh combination (2, 5, 9), the boy across the street must be older than 5. If the boy were 1, 2, 3, or 4, it would contradict the statement.
8. In the eighth combination (3, 3, 10), the boy across the street must be older than 3, but it cannot be older than 10 as there is no combination that would fulfill this requirement.
9. In the ninth combination (3, 5, 6), the boy across the street must be older than 5. If the boy were 1, 2, 3, or 4, it would contradict the statement.
From the above analysis, we can see that the only combination that satisfies all conditions is (2, 3, 15). Therefore, the ages of the children are 2, 3, and 15.
Now, let's find the house number. Since the sum of their ages is the same as the house number, it is 2 + 3 + 15 = 20. Hence, the house number is 20.
Finally, we can determine the age of the boy across the street. We know that he is older than the oldest child, which is 15. Therefore, the age of the boy across the street is greater than 15, but we cannot determine the exact age from the given information.
In conclusion:
The ages of the children are 2, 3, and 15.
The house number is 20.
The age of the boy across the street is unknown (but older than 15).