The complete riddle is a full verse:
विराटनगरे रम्ये कीचकादुपकीचकम् ।
अस्य क्रियापदं वक्त्रे हैमं दास्यामि कङ्कणम् ।।
The first reading means a incomplete sentence without a verb : In the beautiful city of विराट from कीचक to उपकीचक as explained by Mr.Aravind. The second haf says that I will give the person a golden bangle (हैमं कङ्कणम्) to the person who will tell the verb in this sentence.
Now, second readng will give the verb making the sentence complete with a verb and this time you will hope to get the golden bangle (in the first reading).
But reading carefully you will get the meaning:
विः - आट a bird was roaming, in the beautifull city, from a bamboo tree to another bamoo tree (कीचक means bamboo tree). The sentence is complete. If you read second time the second half, हैमं कं कणम् a drop of water and you will not get golden bangle.