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THE CHILDREN ARE 1, 6 AND 6 YEARS OLD. THE PRODUCT OF THEIR AGES IS 36, SO NONE OF THEM CAN BE OLDER THAN 36. THE NUMBER 36 HAS TO BE EXPRESSED AS THE PRODUCT OF 3 NUMBERS. THEIR POSSIBLE AGES ARE (THE SUM OF THEIR AGES IS IN BRACKETS): 1, 1, 36 (3938) 1, 2, 18 (21) 1, 3, 12 (16) 1, 4, 9 (14) 1, 6, 6 (13) 2, 2, 9 (13) 2, 3, 6 (11) 3, 3, 4 (10) SINCE CHERYL IS TOM'S NEXT DOOR NEIGHBOUR, TOM KNOWS CHERYL'S HOUSE NUMBER. TOM WOULD KNOW THE CHILDREN'S AGES IN EVERY CASE THAT SUMS UP TO A UNIQUE NUMBER EXCEPT FOR THE SUM OF 13, WHICH HAVE 2 COMBINATIONS OF POSSIBLE AGES. AS A RESULT, TOM WOULD BE CONFUSED AS HE HAS TO PICK BETWEEN THE 2 COMBINATIONS: (1,6,6) AND (2,2,9). CHERYL THEN TELLS TOM ABOUT HER YOUNGEST CHILD WHO LIKES STRAWBERRY MILK WHICH TELLS TOM THAT THERE IS ONLY 1 YOUNGEST CHILD THE MESSENGER HAS TO HAVE TRAVELED 2 KM. IT DOESN'T MATTER WHAT SPEED THEY WALKED AT. AT THE BEGINNING OF THE PUZZLE, THE LINE IS 1 KM LONG. THE GENERAL IS THEREFORE 1 KM AHEAD OF HIM. THE MESSENGER MUST THEREFORE TRAVEL MORE THAN 1 KM TO REACH THE GENERAL. SINCE THE LINE MOVES 1 KM FORWARD, THE END IS WHERE THE BEGINNING WAS. EVEN IF HE WALKED 1.5 KM TO THE GENERAL, HE ONLY HAS TO WALK 0.5 KM TO GET BACK TO THE END OF THE LINE. IT GOES FASTER GOING BACK, BECAUSE NOW THEY ARE COMING TOWARDS HIM, AND NOT GOING AWAY FOR THE TRAIN TO PASS COMPLETELY THROUGH THE TUNNEL, IT MUST TRAVEL 2 MILES. AFTER 1 MILE TRAVEL, THE TRAIN WOULD BE COMPLETELY IN THE TUNNEL, AND AFTER ANOTHER MILE IT WOULD BE COMPLETELY OUT AND SINCE THE TRAIN IS TRAVELING AT 1 MILE A MINUTE, IT WILL TAKE 2 MINUTES TO PASS THROUGH THE TUNNEL YOU CAN GET 833 APPLES TO BANANAVILLE. FIRST YOU HAVE TO MAKE 3 TRIPS OF 1,000 APPLES FOR 333 MILES. YOU WILL BE LEFT WITH 2,001 APPLES AND 667 MILES TO GO. NEXT YOU HAVE TO TAKE 2 TRIPS OF 1,000 APPLES FOR 500 MILES. YOU WILL BE LEFT WITH 1,000 APPLES AND 167 MILES TO GO (YOU HAVE TO LEAVE AN APPLE BEHIND). FINALLY, YOU TRAVEL THE LAST 167 MILES WITH ONE LOAD OF 1,000 APPLES AND ARE LEFT WITH 833 APPLES IN BANANAVILLE