### Letter of recommendation

**Problem 194** — Putting two and two together can give you a variety of answers, as this month’s problem by Walter Gregg of Chicago demonstrates.

The agile spy once again leaped out of sight (See PTD June ’95.) as Detective Inspector Schnoop bent over his fallen comrade. The wounded officer could only gasp, “One plus two plus four equals seven! One plus two plus four equals seven!”

“Smedley, who was he?”

“One plus two plus four equals seven!” The officer then fell unconscious. Schnoop had been on the case for six months. He had tracked down the bank through which the money had been funneled and had learned that millions had been deposited that very day. All he needed was the account number to begin tracing where the money came from. Earlier in the day, the officer had taped a call from the spy, “ ... are eight. One plus two plus four equals seven.”

Schnoop had a feeling of deja vu and wrote: **R** = 8. He then wrote down the following:

If each leter stands for a unique number between 0 and 9, inclusive, what was the account number?

*Technical consultant, Jack Couillard, Menasha, Wis.*

**Solution to last month’s problem 193** — You know the right angle if you answered **29.4 ft**. Here’s how Stinnt’s foundation grant ran out:

Draw a diagram and label it. Let x be the width of the floor. Since Triangle *BDE* and Triangle *ABE* are right triangles,

Triangle *DCE* and Triangle *ABC* are similar triangles with equal angles. The following relationships apply:

Substituting (4) and (5) into (6):

**Continue on page 2**

Since (*AB*)^{2} – 9 (*DE*)^{2} = 675 in (3) we can construct a right triangle as follows:

Using a trigonometry table, you can scan down the columns adding sines and tangents. At 60 deg the sine and tangent add up to 2.598. Now, from the triangle in (11):

The scene behind the set was more colorful than the scene in front!

**Contest winner** — Congratulations to Alan Smith of Lexington, Ky., who won our March contest by having his name drawn from the 296 contestants who answered correctly out of a total of 356 entrants for that month. A TI-85 calculator is in the mail to him.

The TI-85 Graphing Calculator from Texas Instruments solves for any variable in an equation, can solve 30 simultaneous equations, and finds the roots of a polynomial up to the 30th order. It handles complex numbers in addition to matrices, vectors, lists, and strings. You can perform graphic investigations of almost any type of problem — functions as well as parametric, polar, and differential equations.