Click image to enlarge, maybe.
This is from the occidental mystic mathematician RamanuJohn, and he got it from the University of Massachusetts Mathematics Department Alumni Newsletter.
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One of the following numbers is a perfect square and the others aren't. Using only paper and pencil (no calculators, computers, etc.), determine which is the perfect square. Justify your answer.
a) 176854927
b) 262083721
c) 296837263
d) 322214835
e) 761823600
4 comments:
24 hours is up. This is actually not that hard.
The answer is b) 262083721.
Step 1: eliminate answers A and C, no squared whole number could end in 7 or 3.
Step 2: B could end in either 1 or 9, D could end in 5 and E in 0. This makes B the front runner.
Step 3: The square root is between 10,000 and 20,000 so a good place to start is 15,000 (225000000. close.
Step 4: 16,000 would be 232000000). Very Close.
Step 5: 16,200 (262440000)
16,100 (234210000) which would place it just below 16,200 and ending in 1 or 9.
Step 6: 16,191 Which can be eliminated when the last 3 digits are ....481.
Step 7: 16,189 x 16,189 = 262,083,721.
Note: a number ending in 9 is the logical choise. Not mathamatically logical, but "problem designed by a mathamatician" logical.
Holy krap!
VAMRI (the Vleeptron Advanced Mathematics Research Institute) will have to verify this, of course, but it looks like the cannoli is yours!
You're sure you didn't phone Klaas in Rotterdam?
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