Category: Puzzles

Math Homework

Section: Brain Teasers Category: Mathematics
Difficulty:

A student was given math homework consisting of the following three problems. What is so special about this homework?

  1. What would the value of 190 in hexadecimal be?
  2. Twenty-nine is a prime example of what kind of number?
  3. At time t = 0, water begins pouring into an empty tank so that the volume of water is changing at a rate V’(t)=sec²(t). For time t = k, where 0 < k < π/2, determine the amount of water in the tank.

The answer to each of the problems in the homework is hidden within the question itself:

  1. What would the value of 190 in hexadecimal be?
    The answer is be.
  2. Twenty-nine is a prime example of what kind of number?
    The answer is prime.
  3. At time t = 0, water begins pouring into an empty tank so that the volume of water is changing at a rate V’(t)=sec²(t). For time t = k, where 0 < k < π / 2, determine the amount of water in the tank.
    The answer is tank.
Source:

Math Horizons, MAA

raymond-greenwell
Raymond Greenwell, Head-Royce School Math Club and Rheta Rubenstein September 19, 2022
0 Comments

A Very Cool Number

Section: Brain Teasers Category: Mathematics
Difficulty:

Find a number containing every digit 0-9 exactly once, such that for every 1≤N≤10, the leftmost N digits comprise a number, divisible by N.

Let the number be ABCDEFGHIJ.

  • The digit J must be 0, so that the number is divisible by 10.
  • The digit E must be 5, so that the number comprised of the first 5 digits is divisible by 5.
  • The digits B, D, F, H, J must be even, and therefore the digits A, C, E, G, I must be odd.
  • The numbers CD and GH must be divisible by 4 and the number FGH must be divisible by 8. Since C and G are odd, D and H must be 2 and 6, or vice-versa.
  • Since ABC, ABCDEF, and ABCDEFGHI are all divisible by 3, we see that A+B+C, D+E+F, and G+H+I are divisible by 3 as well. Therefore, D+F+5 is divisible by 3 and since D and F are even, we have either D=2, H=6, F=8, B=4 or D=6, H=2, F=4, B=8.
    • D=2, H=6, F=8, B=4. Since FGH is divisible by 8 and G is odd, we have G=1 or G=9. Also, G+I+6 is divisible by 3 and since I is odd, we have G=1, I=3. The only possibilities for ABCDEFG are 7492581630 and 9472581630, but they are not divisible by 7.
    • D=6, H=2, F=4, B=8. Since FGH is divisible by 8 and G is odd, we have G=3 or G=7. Also, G+I+2 is divisible by 3 and since I is odd, we have G=3, I=1 or G=3, I=7 or G=7, I=3 or G=7, I=9. The only possibilities for ABCDEFG are 9876543, 7896543, 1896543, 9816543, 1896547, 9816547, 1836547, 3816547. Out of these, only 3816547 is divisible by 7.

We conclude that the only solution is 3816547290.

lea-gorodisky
Lea Gorodisky September 10, 2022
0 Comments

More Sisters on Average

Section: Brain Teasers Category: Mathematics
Difficulty:

Who have more sisters on average in a society: boys, girls, or is it equal?

Remark: Assume that each child is born a boy or a girl with equal probability, independent of its siblings.

The average number of sisters is roughly the same for both boys and girls. To see this, notice that every girl in every family contributes “one sister” to each of its siblings who are either a boy or a girl with equal probability. Therefore, every girl contributes on average the same number of sisters to the group of boys and to the group of girls. Since there is roughly the same number of boys and girls in the society, the average number of sisters for boys and girls is the same.

unknown-author
Unknown Author September 1, 2022
0 Comments

The Car and the Bird

Section: Brain Teasers Category: Insight
Difficulty:

A car weighing 1500kg (including the driver) starts crossing a 20km long bridge. The bridge can support at most 1500kg and, above that weight, it collapses. If halfway through the bridge, a small bird, weighing 200g, lands on the roof of the car, will the bridge collapse?

By the time the car reaches the middle of the bridge, it would have used fuel that weighs more than 200g, so the bridge will not collapse.

unknown-author
Unknown Author August 28, 2022
4 Comments

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