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Last month's solutions
Solution: The only twodigit numbers that add to thirteen is 49, 58, 67, 94, 85 and 76. Of these, the only number with an odd number of divisors is 49 (7 x 7) (1 divisor). The other numbers either have no divisors or an even number: 58 (2 & 29), 67 (none), 94 (2 & 47), 85 (5 & 17) and 76 (2, 4, 19 & 38) (none, 2 or 4) Therefore, my favourite number is 49 (with only one divisor). 
Solution: Let x = number of senior students and y = sum of freshmen and sophomore students Then, y = ¼ (freshmen) + 1/3 (sophomores) y = ¼ (336) + 1/3 (336) = 84 + 112 =196 and x = 336 – y – ½ (336 – y) = 336 – 196 – ½ (140) = 70 senor students 
Solution: Circumference of cutter = πD1 = ¾ π Circumference of can = πD2 = 2½ π Number of turns = πD2 / πD1 = 2½ π / ¾ π = 5/2 ÷ ¾ = 5/2 x 4/3 = 20/6 = 3 & 1/3 turns 
Solution: For the floor area of 315 one dimension must end in a 5 (i.e., 5, 15, 25, etc.). The best fit is 15 and therefore the floor dimensions would then be 15 ft. x 21 ft. Then, for one side area of 120 sq. feet wall, one dimension must be either the 15 ft. or 21 ft. The best fit is 15 and therefore the the wall dimensions would then be 15 ft. x 8 ft. And for the other side area of 168 sq. feet wall, one dimension must be 21 ft. The other wall dimensions would then be 21 ft. x 8 ft. Therefore, the volume for the room = 15 x 21 x 8 = 2,520 cubic feet. 