## Which house?

**The Ng family bought house number 10.**

**Solution:**

**How do we work it out?**The even numbers from 2 to 12 are 2, 4, 6, 8, 10, 12.

As the grandparents bought houses at opposite ends of the street, one set of grandparents bought house number 2 and the other set of grandparents bought house number 12.

To work out the next steps we need to know what multiples and factors are. Factors are the whole numbers we can multiply to get a number, for example 3 x 4 = 12, with 3 and 4 factors of 12. Multiples are the numbers we get after multiplying whole numbers, for example 3 x 4 = 12, with 12 a multiple of 3 and 4.

The Lee family bought a house which is a multiple of three. This means their house number may be obtained by multiplying 3 by a certain number. The only house numbers that are a multiple of 3 are number 6 (2 x 3) and number 12 (4 x 3). As one of the grandparents bought house number 12, the Lee family must have bought house number 6.

As four is a factor of the house number bought by the Shin family, the house numbers with a factor of four are 4 (1 x 4), 8 (2 x 4) and 12 (3 x 4). As one of the grandparents bought house number 12, the Shin family may have bought house number 4 or 8.

As the Kim family bought

*the*house (meaning there is only one house) between the Lee family (at house number 6) and one of the sets of grandparents, they must have bought house number 4. That means the Shin family cannot have bought house number 4 and must have bought house number 8.

The only house left, bought by the Ng family, is house number 10.