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YES, THERE IS A POINT ALONG THE PATH THAT THE MONK OCCUPIES AT PRECISELY THE SAME TIME ON BOTH DAYS. IF YOU ASSUME THAT THE THERE ARE TWO MONKS, ONE DOES THE ROUTE FROM THE TOP, AND THE OTHER FROM THE BOTTOM. AT SOME POINT, THEY MUST MEET. THERE'S YOUR POINT 28 DAYS. UNTIL THE 27TH NIGHT, THE FROG WOULD HAVE MANAGED TO SCALE A HEIGHT OF 1 METER PER DAY OR 27 METER IN TOTAL. ON THE 28TH DAY, HE WOULD HAVE CLIMBED 3 METERS DURING THE DAY THEREBY COMPLETING HIS TASK HE HAD 15 EGGS. THE FIRST PERSON BOUGHT HALF OF THE 15 EGGS WHICH IS 7½ EGGS AND ANOTHER ½ EGG. SO HE BOUGHT 8 EGGS IN TOTAL AND JACK IS LEFT WITH 7 EGGS. THE SECOND PERSON BOUGHT HALF OF THE REMAINING 7 EGGS WHICH IS 3½ EGGS AND ANOTHER ½ EGG. SO HE BOUGHT 4 EGGS AND JACK IS LEFT WITH 3 EGGS. THE LAST PERSON BOUGHT HALF OF THE REMAINING 3 EGGS WHICH IS 1½ EGGS AND ANOTHER ½ EGG. SO THE LAST PERSON BOUGHT 2 EGGS. THAT LEAVES 1 EGG REMAINING IN JACK'S BASKET THE MAN MAKES AN OVERALL PROFIT OF $200. THE MAN ALWAYS SOLD THE HORSE FOR A $100 PROFIT EVERY TIME. ASSUME THAT HE HAD $1000 IN THE BEGINNING. AFTER BUYING THE HORSE FOR $600 AND THEN SELLING IT OFF FOR $700, HE WOULD HAVE: $1000 - $600 - $700 = $1100. AFTER BUYING THE HORSE FOR $800 AND THEN SELLING IT OFF FOR $900, HE WOULD HAVE: $1100 - $800 + $900