#61 - Pilot Problem
Lavesh was piloting a plane behind a car but was never able to overtake it. Why?
The car was in a merry go round.
#62 - Magnet Problem
You are in a room with no metal objects except for two iron rods. Only one of them is a magnet.
How can you identify which one is a magnet?
You can hang the iron rods on a string and watch which one turns to the north (or hang just one rod).
Gardner gives one more solution: take one rod and touch with its end the middle of the second rod. If they get closer, then you have a magnet in your hand.
The real magnet will have a magnetic field at its poles, but not at its center. So as previously mentioned, if you take the iron bar and touch its tip to the magnet's center, the iron bar will not be attracted. This is assuming that the magnet's poles are at its ends. If the poles run through the length of the magnet, then it would be much harder to use this method.
In that case, rotate one rod around its axis while holding an end of the other to its middle. If the rotating rod is the magnet, the force will fluctuate as the rod rotates. If the rotating rod is not magnetic, the force is constant (provided you can keep their positions steady).
#63 - Birthday Problem
The day before yesterday I was 25 and the next year I will be 28. This is true only one day in a year. What day is my birthday?
He was born on December 31st and spoke about it on January 1st.
#64 - Mathematical Fraction Problem
Find a 9-digit number, which you will gradually round off starting with units, then tenth, hundred etc., until you get to the last numeral, which you do not round off. The rounding alternates (up, down, up ...). After rounding off 8 times, the final number is 500000000. The original number is commensurable by 6 and 7, all the numbers from 1 to 9 are used, and after rounding four times the sum of the not rounded numerals equals 24.
473816952 – if rounding changes the next numeral character
#65 - Mathematical Fraction Problem
Using four sevens (7) and a one (1) create the number 100. Except the five numerals you can use the usual mathematical operations (+, -, x, :), root and brackets ()
100 = 177-77 = (7+7)x(7+(1:7))
#66 - Mathematical Fraction Problem
Rectify the following equality 101 - 102 = 1 by moving just one digit.
101 - 102 = 1.
#67 - Mathematical Roundoff Problem
Find a 9-digit number, which you will gradually round off starting with units, then tenth, hundred etc., until you get to the last numeral, which you do not round off. The rounding alternates (up, down, up ...). After rounding off 8 times, the final number is 500000000. The original number is commensurable by 6 and 7, all the numbers from 1 to 9 are used, and after rounding four times the sum of the not rounded numerals equals 24.
473816952 - if rounding changes the next numeral character.
#68 - Mathematical Number Problem
What 5-digit number has the following property? If we put numeral 1 in front of the number, we get a number three times smaller, than if we put the numeral 1 behind this number.
Using an easy equation: 3(x+100000) = 10x+1 we find out that the number is 42857.
#69 - Time By cents Problem
man gave one son 10 cents and another son was given 15 cents. What time is it?
1:45. The man gave away a total of 25 cents. He divided it between two people. Therefore, he gave a quarter to two.
#70 - Mathematical Problem
What is the four digit number in which the first digit is one-third the second, the third is the sum of the first two, and the last is three times the second?
1349