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2(3sec2 20 sin2 10)1/3

The expression above can be expressed in the form a + bsec 20. Find a and b.
(No Solution Yet, 0 Comments) Submitted on 2018-04-22 by Danish Ahmed Khan    

DO+SI=MI
RE+MI=FA
LA+SI=SOL

Solve to get the unique answer.
(Solution Posted, 2 Comments) Submitted on 2018-04-21 by Ady TZIDON    

A tetrahedron with five edges of unit length is inscribed in a unit sphere. How long is the sixth edge?
(No Solution Yet, 2 Comments) Submitted on 2018-04-20 by Danish Ahmed Khan    

primer+rimer+imer+mer+er+r=malaga

There is only one valid solution for the above alphametic.

Find it.

(No Solution Yet, 1 Comments) Submitted on 2018-04-19 by Ady TZIDON    

Five delegates to an international conference, Alex, Boris, Chris, Daniel and Eva, among them spoke five languages. In fact one of them spoke only one of the languages; one spoke only two of them; another, only three; another spoke four of the languages and finally one spoke all five of the languages.

The following are true about which languages were spoken:

  1. Three of the delegates spoke Portuguese.
  2. Spanish was spoken by more of the delegates than any other language.
  3. When Chris and Eva conversed, it had to be in Italian--the only language that both spoke.
  4. The only common language among Alex, Boris and Eva was French.
  5. Boris and Chris both spoke English, but when Daniel joined them, they had to switch to Spanish, the only language common to all three.

What languages did each of the delegates speak?


From Marilyn vos Savant's column in Parade magazine for April 15, 2018.
(No Solution Yet, 1 Comments) Submitted on 2018-04-18 by Charlie    

If A1, A2, A3, . . . , A30 are the vertices of a regular 30-gon inscribed in a unit circle, then find

|A1A2|2 + |A1A3|2 + |A1A4|2 + ... + |A1A30|2
(No Solution Yet, 3 Comments) Submitted on 2018-04-17 by Danish Ahmed Khan    

A certain device consists of 24 equally reliable components. It is known that one (and only one) is faulty. The location of the failed component is performed by replacement - one after another.

1. Find the probabilty of restoring the functioning of the system within 3 trials.
2. Same question for n trials.

(Solution Posted, 5 Comments) Submitted on 2018-04-16 by Ady TZIDON    

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