> There are three distinct digits that can be arranged to make product > of two distinct primes. In fact, all six arrangements give the > product of two distinct primes. Can you find the smallest of these > numbers? 178. (My first guess was 134, a near miss, as all the permutations are products of two primes except the largest, which is the prime 431.) -- Roger Phillips ------------------------------------------ Ed, I'm not sure if you're looking for the smallest of the digits, which is 1, or the smallest of the products, which is 178. It was a fun puzzle, but I'm curious if there is an easier method than mine (I used Excel to do the multiplying, then visually inspected the results). Tom Clymer ------------------------------------------ Ed, I'm not sure if this is the question you asked, but the three digits 1,7, and 8 take in the six combinations all factor into a product of two primes: 178 = 2 * 89 187 = 11 * 17 718 = 2 * 359 781 = 11 * 71 817 = 19 * 43 871 = 13 * 67 Kirk Bresniker ------------------------------------------ 178 =2*89 187=11*17 718=2*359 781=11*71 817=19*43 871=13*67 James L Melby ------------------------------------------ 178 is a solution.. any others? great website, Jason ------------------------------------------ {1,7,8} isthe solution. So 178 is the answer Les shader ------------------------------------------ 178 I made the assumption that 0 would not be allowed, since you say all six arrangements of these digits are the product of two primes, and numbers starting with 0 are usually not allowed. That means there are only 84 possible sets of digits. Searching by hand starting from 123 found the solution fairly quickly. -- Eric Backus ------------------------------------------ 178 Andrew Lord ------------------------------------------ 178 One of the permutations is a movie title. (One Eight Seven) Bryce Herdt ------------------------------------------ 178 = 2 * 89 187 = 11 * 17 718 = 2 * 359 781 = 11 * 71 817 = 19 * 43 871 = 13 * 67 Colin Sturm ------------------------------------------