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ONE THING JULIE COULD DO IS FREEZE A TRAY OF ICE-CUBES, AND TURN THE TRAY OF ICE UPSIDE DOWN IN HER FREEZER. WHEN SHE COMES HOME, SHE SHOULD CHECK THE TRAY. IF THE ICE CUBES ARE STILL IN THE TRAY, THE FOOD IS SAFE TO EAT. IF THE TRAYS ARE EMPTY, IT'S TIME TO CLEAN OUT THE FREEZER. SHE WILL HAVE TO MAKE A JUDGMENT CALL IF THE ICE-CUBES ARE ONLY SLIGHTLY THAWED BEFORE I LEFT, I WOUND THE WALL CLOCK. WHEN I RETURNED, THE CHANGE IN TIME EQUALED HOW LONG IT TOOK TO GO TO MY FRIENDS HOUSE AND RETURN, PLUS THE TIME I SPENT THERE. BUT I KNEW THE LATTER BECAUSE I LOOKED AT MY FRIENDS WATCH WHEN I ARRIVED AND LEFT. SUBTRACTING THE TIME OF THE VISIT FROM THE TIME I WAS ABSENT FROM MY HOUSE, AND DIVIDING BY 2, I OBTAINED THE TIME IT TOOK ME TO RETURN HOME. I ADDED THIS TIME TO WHAT MY FRIEND WATCH SHOWED WHEN I LEFT, AND SET THE SUM ON MY WALL CLOCK 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 400 MILES. WORKING BACKWARDS, ON THE FINAL DAY TOM CYCLED THE REMAINING 5 MILES. ON DAY 5, HE STARTED WITH 15 MILES (CYCLED TWO THIRDS, LEAVING 5 MILES). ON DAY 4, HE STARTED WITH 25 MILES (CYCLED 10 MILES). ON DAY 3, HE STARTED WITH 100 MILES (CYCLED THREE QUARTERS, LEAVING 25 MILES). ON DAY 2, HE STARTED WITH 200 MILES (CYCLED HALF, LEAVING 100 MILES). ON DAY 1, HE STARTED WITH 400 MILES (CYCLED HALF, LEAVING 200 MILES)