When a careful count was taken a few years back, the Timbuktu Post Office handled at least 3120 letters and 1890 advertising brochures daily. The canceling machine then in use could handle 390 letters and 315 brochures per hour at an hourly cost of $2.10. The post office was planning to acquire a new and improved model which could handle 520 letters and 210 brochures per hour at a cost of $2.70 per hour. Neither machine could be run for more than 10 hours per day due to internal heating. Neither machine could handle more than the maximum per hour in either category. For example, if the current machine was canceling only brochures, it still couldn’t handle more than 315 brochures per hour, and it still couldn’t run more than 10 hours per day without melting down. With these constraints, what would be the most economical way to run the post office canceling operation if they purchased the new machine?
Puzzles, Riddles, and Systematic Thinking
Cubic Factoring
If a ≠ b, a3 – b3 = 19x3, and a – b = x, which of the following conclusions is correct?
- a = 3x
- a = 3x or a = -2x
- a = -3x or a = 2x
- a = 3x or a = 2x
- a = 2x
Powers of n + i
Given that i2 = -1, for how many integers n is (n + i)4 an integer?
Four 4’s: 1 – 20
You are to find expressions for each whole number from 1 through 20, using in each expression exactly four 4�s, plus any mathematical symbols you like: parentheses, plus signs, etc.
| Sample: | 1 = | 4 + 4 | . |
| 4 + 4 | |||
Four 4’s: 21 – 40
In a previous problem, you found mathematical expressions equalling each of the numbers 1 – 20 using exactly four 4’s and any mathematical symbols you wanted to. Now make 21 – 40 following the same rules.
Six 9’s Make 100
Use six 9’s to make a numerical expression that equals 100.
Parentheses Insert
Insert parentheses to make the following equation true:
2 · 1 + 2 · 3 – 2 · 2 – 1 = 12
Maximum Product, Use All Digits
Using each of the 10 digits once, find two 5-digit numbers with the largest possible product.
Product = TTT
In the following equation, each of the letters represents a uniquely different digit in base ten. Suppose:
(YE)(ME) = TTT, where the number YE is less than ME in the product on the left.
Then the sum E + M + T + Y equals:
- 19
- 20
- 21
- 22
- 24
Chinese Restaurant Party
At a large party in a Chinese restaurant (Wok Around the Clock), every three guests used a bowl of rice among them, every four guests used a bowl of soup among them, and every pair of guests used a bowl of fish between them. There were 65 bowls of these three things altogether. How many guests were at the party?