Strange number

34

F98. What is the maximum difference in potential power to obtain if you have a source with e.g. d.s. $E$ and $n$ identical capacitors with a capacity of $c$ each?

L. G. Aslamazov

F99. figure 3 shows $V$—$T$ diagrams for two circular processes. In which of them does the gas do more work: in process $1 \rightarrow 2 \rightarrow 3 \rightarrow 1$ or in process $1 \rightarrow 3 \rightarrow 4 \rightarrow 1$?

I. Sh. Slobodetsky

F100. At an altitude of 200 km, the atmospheric density is $1,6 \cdot 10^{-10} \text{ ке/м}^3$. Estimate the drag force experienced by a satellite of cross-section $0,5 \text{ m}^2$ and mass $10 \text{ ке}$ flying at this altitude.

F101. A ball is suspended from a hanging light spring with stiffness $k$. At first the spring does not grow. Then the ball is released. What is the maximum speed the ball will reach while moving? The mass of the ball is $m$.

S. A. Belleev

F102. Oxygen and helium were mixed equally in a hermetically sealed vessel. Then small responsible ones were made in the wall of the vessel. What is the composition of the molecular beam emerging from it?

I. Sh. Averbukh

In this issue we feature several problems from Scientific American magazine in the Mathematical Games section. The permanent editor of Mathematical Games is Martin Gardner. The problem on the fourth page of the cover is also taken from this section. (Translation by I. I. Moroz).

PLACE THE COINS

This little challenge was created by Kobon Fujimura from Japan. Place the ten coins as shown at figure. What is the maximum number of coins you must remove so that there is not a single equilateral triangle (of any size) with vertices in the centers of the remaining coins?

STRANGE NUMBER

Find a tenth number in which its first digit indicates the total number of zeros in the number, the second - the total number of ones, and so on until the last digit indicates the number of nines in the number (of course, zero is a digit). There is only one solution.