How many times will your heart beat this month?
Set 02
Egyptian Fractions
Egyptian fractions were typically written in terms of unit fractions, that is, fractions with a numerator of 1. With the exception of a few common, simple fractions like 2/3, non-unit fractions were decomposed into sums of distinct unit fractions.
Examples:
.
Write these fractions as Egyptian fractions:
Sum of Big Fractions
Find this sum without using a calculator. There is a swift way to do it.
- 0
Guess the Number
Find a number that satisfies these conditions: The number has 5 digits. Two of the digits are zeros. The sum of the digits is 20. The digit in the thousands’ place is not zero, and it is three times the digit in the tens’ place. What is the number?
Gym Class
A co-ed gym class has 50 students. Some are left-handed and some are right-handed (of course). If 23 students are boys, 36 students are right-handed, and there are 4 left-handed girls, then how many right-handed boys are there?
Tennis Playing Family
A woman, her brother, her son, and her daughter (all relatives by birth) are tennis players. The worst player’s twin (who is one of the four players) and the best player are of the opposite sex. The worst player and the best player are the same age. Who is the worst player?
- the woman
- her son
- her brother
- her daughter
- No solution is consistent with the given information.
Super Duper Market
Three boys — Denis, Troy, and Memo — all work at the Super Duper Market after school each day. They either stock shelves or they bag the customers’ groceries at the cash register. Each day Mr. Chive, the store manager, decides which boy will do what by these rules:
- Either Denis or Memo, but not both, will stock shelves;
- If Denis stocks shelves, then Troy will bag groceries;
- Troy and Memo will not both bag groceries.
Which of the three boys could have stocked shelves yesterday AND could be bagging groceries today?
Brothers and Sisters
A 14-year-old boy says, “I have as many brothers as I have sisters.” His sister says, “I have twice as many brothers as sisters.” How many brothers and sisters are in this family?
Send More Money
Each different letter in this famous problem stands for a different digit (but the same letter always stands for the same digit). A girl sent this message home from camp after she had spent her entire summer allowance on the very first day. Figure out what each letter stands for.
Crossnumber Puzzle 1
Across
1. All digits are odd and all are different.
5. Sum of the digits is half the cube root of 3 down.
6. A prime number.
8. This number is three times the sum of its digits.
9. This number reversed is the square of an even number.
11. Is the same number when reversed and is divisible by 9.
1. All digits are odd and all are different.
5. Sum of the digits is half the cube root of 3 down.
6. A prime number.
8. This number is three times the sum of its digits.
9. This number reversed is the square of an even number.
11. Is the same number when reversed and is divisible by 9.
Down
1. First three digits are the first three digits of 4 down rearranged.
2. A prime number.
3. A perfect cube.
4. Each digit is greater than the preceding one.
7. A multiple of 8 across.
10. The sum of the digits is the square of a perfect square.
1. First three digits are the first three digits of 4 down rearranged.
2. A prime number.
3. A perfect cube.
4. Each digit is greater than the preceding one.
7. A multiple of 8 across.
10. The sum of the digits is the square of a perfect square.
(Note: There are no zeros in any of the cells.)
