Puzzle:

In the equation shown below, A, B, C, D, and E are 5 consecutive positive integers. What are they?

A*A + B*B + C*C = D*D + E*E

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Solution:

A=10, B=11, C=12, D=13, E=14.

10x10 + 11x11 + 12x12 = 13x13 + 14x14

A=10, B=11, C=12, D=13, E=14.

10x10 + 11x11 + 12x12 = 13x13 + 14x14

## 12 comments:

10, 11, 12, 13, 14

Hi Suman/Jayanth

Can u explain the way of solving these type of puzzles?

SEAM * T = MEATS

10,11,12,13,14... Simple quadratic equation formulation...

@PG...

As suggested by some, one way would be to write a brute-force (or maybe even some intelligent program) to do it...

Usually best languages to write such programs would be some mathematical/logical programming language (like PROLOG, LISP) or maybe some scripting like PERL etc...

But if you want to proceed manually, find out the various constraints, and then try to reduce the solution space for each variable... For example in this case, we have :

T*M % 10 = S, so you can find the possible combinations of T, M and S...That reduces the possible cases alot...Also, M != 0 and neither M nor T equal 1 (because otherwise M*T would either equal M or T)...so you build all the cases you can come up with :), and then use a bit of back-tracking as you pick one particular case :)...So basically,

Build cases/rules/constraints first...

Hope that helps

a^2+(a+1)^2+(a+2)^2=(a+3)^2+(a+4)^2;

solve this quadratic equ.

a=10 ans

10 11 12 13 14 15

sorry

10 11 12 13 14

SEAM * T = MEATS

Solution:

4973 x 8 = 39784

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