Five kinds of flowers grow in separate gardens on five different streets. Here is what you know:
1. The Smiths do not grow violets.
2. The Morgans grow peonies and do not live on 2nd street.
3. The Parks live on 3rd street.
4. Begonias bloom on 4th street.
5. Roses do not grow on 5th street.
6. The Johnsons do not live on 1st street.
7. The Rosens do not grow daffodils
8. The Johnsons grow roses
9. Daffodils grow on 1st street
Which flowers grow on in whose gardens on what streets?
You have a fox, a chicken and a sack of grain. You must cross a river with only one of them at a time. If you leave the fox with the chicken he will eat it; if you leave the chicken with the grain he will eat it. How can you get all three across safely?
Take the chicken over first. Go back and bring the grain next, but instead of leaving the chicken with the grain, come back with the chicken. Leave the chicken on the first side and take the fox with you. Leave it on the other side with the grain. Finally, go back over and get the chicken and bring it over.
Find a six-digit number containing no zeros and no repeated digits that satisfies the following conditions:
1. The first and fourth digits sum to the last digit, as do the third and fifth digits.
2. The first and second digits when read as a two-digit number equal one quarter the fourth and fifth digits.
3. The last digit is four times the third digit.
If you call the number ABCDEF, then you get the following equations.
1. A + D = F and C + E = F
2. AB = DE / 4
3. F = 4 × C
The only numbers that work for C and E are 2 and 6 or 4 and 8, and in order to make F a single-digit number, we can deduce that C = 2, E = 6 and F = 8.
So far, our number is AB2D68.
We know A + D = 8 so A and D are both odd numbers. The only odd number less than 8 that we can use for D to make one-quarter of two-digit number D6 also be a two-digit number is 7, so D = 7 and A is 1. This makes the two-digit number AB 19.
