On holiday recently we noticed three towns along the coast were all anagrams of each other; namely, LADEHO, DEHOLA and HOLADE. We all agreed that this was very curious, but could find no explanation, apart from it being a happy coincidence.
Over a beer or two one evening the mathematician in our party discovered something even more curious about these place names. If each of the letters in the three names represents a digit, the following sums are also true:
LADEHO x D = DEHOLA
DEHOLA x D = HOLADE
Although she was quick to point out that this is not really a coincidence.
So what number does LADEHO represent (and thus DEHOLA and HOLADE)? And can you explain why this is not a coincidence?
LADEHO represents the number 142857, and thus DEHOLA is 285714 and HOLADE is 571428.
0.142857 is the recurring decimal for one seventh, well known to mathematicians for this curious property.