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Resolution

Let the puzzle mathematical made four days ago. We'll see how today - using the Solver of Excel - you can easily solve this problem, although the algebra is not your forte ...

The model below shows the original formulas in column A, and how we have entered into the model C3: F5. The values of the three variables are in line 2. Formula G3 reproduced until line 5 is: = SUMPRODUCT ($ C $ 2: $ F $ 2, C3: F3) .

Formula G6, finally, is: = SUMPRODUCT (G3: G5 G3: G5) . This formula calculates the sum of squared residuals of the equations: it must result in a score of 0 for the problem to be solved.

We then used the solver of Excel by entering the above parameters. It just click on the button "Solve" for a split second in the final solution with C2, C3 and C4 values 40, 30 and 10.

Note - If you do not see the solver to the right of the tab "Data" is that you must activate it. For this, go through the Office button, click "Excel Options" then "supplements" and then select the solver, go through the button "Go" and finally check and validate the solver ...

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A mathematical puzzle ...

For once, we'll just in this paper to present an algebraic puzzle, as we often see in books of games and mathematical problems. We found this puzzle at the following address: http://www.mathforu.com/sujet-10253.html .

"Jack was twice the age that Yann had when Jack was old Yann. When will
Yann Jack age, they will have between them 90 years.
What ages are they? "

The first part of the first sentence is formulated algebraically in
J = 2 * (Ym) , where the variables represent the age of Jack, one of Yann and a number of years apart .

The second part of the first sentence is a formula even simpler: m = J - Y .

The second sentence can be formulated as follows: J + Y + 2 * (JY) = 90 . It is

not necessary to be a light in algebra to find with these three equations - for three unknowns, thankfully! - The final solution:
J = 40 and Y = 30.

Note 1 - What is interesting is to see how long it took - with the exchange reproduced the above address - before the exact solution is discovered ...

Note 2 - What regulars of this blog may be assured that the link between the enigma and Excel will appear in the next article:)