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3333= ?
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x=Number of 1s = 10011111...11111−Number of 2s = 5022222...22222
What is the sum of digits in x?
Hint: Try it with smaller numbers first. For example, find the sum of digits in 111111−222.
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I know that just adding numerators and denominators doesn’t work. For example,
21+32=2+31+2.
Curious if this kind of addition ever works, I look for positive integers a,b,c,d such that
ba+dc=b+da+c.
After some searching, I conclude that such numbers don't exist. Am I right?
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A system of two symmetrical, identical, water-filled jars is fixed on a turntable. Each jar has a cork—attached to the bottom by a thread—floating vertically.
What will happen to the corks when the turntable starts rotating?
Details and Assumptions:
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What is the length of BC?
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