Two scruffy dogs were walking down the street. The first dog turned to the other and said, “Do you realize that if one of your fleas jumped onto me we would have the same number of fleas?” The second replied, “Yes, but if one of your fleas jumped onto me I would have five times as many fleas as you.” How many fleas are on each dog to begin with?
A similar problem can be found in L.A. Graham’s Ingenious Mathematical Problems and Methods with a range of 1 to 9, but the principle remains the same – the numbers with the smallest difference produce the largest product. You start out with the highest two digits, 7 and 6, then attach 5 and 4, putting the smaller of the two digits with the larger number, giving you 74 and 65. The next two highest digits are 3 and 2, giving you 742 and 653. Finally, you add the 1 to the lower number. Page 80 has the details of that solution.
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?