Welcome to Varsity Math, the weekly math puzzle column by the National Museum of Mathematics and featured each weekend in the Wall Street Journal.
A brother and sister own twelve identically shaped solid gold statues that are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, and 12 inches tall.
How can they divide the statues into two sets which have equal total weights?
At the annual faculty meeting, a couple approaches the head of the math department and states “Our three children are all younger than 20. Earlier tonight we told Professor Smith the sum of their ages and the sum of the cubes of their ages and challenged him to tell us how old they are. He got the wrong answer. We gave Professor Jones the same problem two years ago and he got the wrong answer then.” The head of the math department replies, “You’ve told me all I need to know.”
How old are the couple’s children?
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Solutions to week 152
Nuts and Bolts answer explained:
Let n be the price of a nut and b be the price of a bolt. Then 5n × 8b = 5n + 8p = 7.2. This has two solutions with (n, b) = (1.2, .15), or (.24, .75). The second solution has both items priced under a dollar.
Bridge Crossing answer explained:
Persons 1 and 2 go across and Person 1 comes back with the flashlight. This takes 4 min. Persons 5 and 6 go across and Person 2 comes back with the flashlight. This takes 12 min. Persons 1 and 4 go across and Person 1 comes back with the flashlight. This takes 7 min. Persons 1 and 3 go across and Person 1 comes back with the flashlight. This takes 5 min. Persons 1 and 2 go across. This takes 3 minutes and the total elapsed time is 31 min.
Links to all of the puzzles and solutions are on the Complete Varsity Math page.
Come back next week for answers and more puzzles.