Bolts from the blue
PROBLEM 216 – An ounce of prevention isn't always worth a pound of cure, as this month's problem by M.D. Kilgore of Dallas demonstrates.
Way up in the corner office of the Lee Key Hydraulic Co., President Horatio Puff was suavely sipping coffee with his biggest customer, Percy McTwipp.
"Your special-delivery order will be ready in just a few
minutes," commented Puff. "I have my top man, Lucius Bluff, checking on it right now. Your customized bolts will be delivered to you shortly."
Meanwhile down in the stockroom, pandemonium reigned.
The customized bolts were no different than the standard bolts except that they weighed one gram less. The standard bolts each weighed 1 oz. Through Lee Key's usual efficiency, the box of customized bolts got mixed in with the boxes of standard bolts. Each box contains 100 bolts.
"All right," huffed Bluff. "I've narrowed it down to these 10 boxes." He shakily grabbed a scale and began ripping open the boxes. Suddenly he stopped and thought a moment. With confidence he phoned up to Puff and said he would be up in a moment with the box of customized bolts.
Bluff's scale can weigh as many or as few bolts as he wishes and it is accurate to the nearest gram. What is the least number of weighings Bluff needs to make to find the box of lightweight bolts from among the 10 boxes, and what is the logic behind your answer?
SOLUTION TO LAST MONTH'S PROBLEM 215 – You know which side of the road you're on if you answered 40,114 ft2. Here's the lay of the land:
The area occupied by the 400-ft-by 300-ft pasture is equal to the two triangles and a parallelogram created by the road. Let x be the width of road at the edge of the property. Add the areas of the two triangles and the parallelogram:
