Math Riddles

Answer: 43.

After 6 all numbers divisible by 3 can be ordered (because they can all be expressed as a sum of 6's and 9's). After 26, all numbers divisible by three when subtracted by 20 can be obtained. After 46, all numbers divisible by three when subtracted by 40 can be obtained. After 46, all numbers fit into one of these 3 categories, so all numbers can be obtained. 43 is the last number that doesn't fall into one of these categories (44 = 20 + 6 * 4, 45 = 6 * 6 + 9).

Answer: The feathers. A pound of feathers is measured in avoirdupois weight, in which one pound equals 16 ounces. Precious metals are measured in troy weight, in which one pound equals 12 ounces.

However, the ounces are not measured in the same way. In avoirdupois weight, one ounce = 437.5 grains. In troy weight, one ounce = 480 grains.

So, one pound of feathers weighs (16)x(437.5 grains) = 7,000 grains. One pound of gold weighs (12)x(480 grains) = 5,760 grains.

Answer: The numbers are 3 and 4.

Since Sam knows the sum of the numbers (x + y) he would only know the answer immediately if the sum was 4 (2 + 2) or 5 (3 + 2). Then when Pete (who knows x*y) knew that Sam didn't know the answer the product must have several numbers that add up to the sum (7 = 3 + 4, 7 = 5 + 2). When Pete doesn't know the answer at this point we know the product must have more than one pair of viable factors (12 = 3 * 4, 12 = 6 * 2). At this point Sam knows the numbers are 3 and 4 because they are the only numbers that meet these criteria.

Answer: He had to walk backwards

Answer: Neither. 9 and (plus) 5 is 14, not 13.