## Task 3 - 170813

The name of a prominent mathematician is written with five letters. The letters $A, B, C, \ldots, Y, Z$ of the alphabet are assigned the numbers 1, 2, 3, ..., 25, 26 in this order. If we substitute the numbers assigned to the letters of the mentioned name, the sum of the

(1) numbers assigned to the first and second letters is 26,

(2) numbers assigned to the first and third letters is 17,

(3) numbers assigned to the first and fourth letters is 10,

(4) numbers assigned to the first and fifth letters is 23,

(5) numbers assigned to all five letters is 61.

Determine the name of this mathematician!
Let the number assigned to the first letter of the sought name be $x$. Then, due to

(1) the number assigned to the second letter is $(26-x)$,

(2) the number assigned to the third letter is $(17-x)$,

(3) the number assigned to the fourth letter is $(10-x)$,

(4) the number assigned to the fifth letter is $(23-x)$.

Because of (5), one thus obtains

$$
x+(26-x)+(17-x)+(10-x)+(23-x)=61
$$

from which $x=5$ follows.

The numbers assigned to the five letters of the sought name are therefore, in sequence, 5, 21, 12, 5, 18. Their replacement by the letters of the alphabet to which they are assigned yields:

E, U, L, E, R. The sought name of the mathematician is Euler.