Find a six-digit number containing no zeros and no repeated digits that satisfies the following conditions:
1. The first and fourth digits sum to the last digit, as do the third and fifth digits. 2. The first and second digits when read as a two-digit number equal one quarter the fourth and fifth digits. 3. The last digit is four times the third digit.
If you call the number ABCDEF, then you get the following equations.
1. A + D = F and C + E = F 2. AB = DE / 4 3. F = 4 × C
The only numbers that work for C and E are 2 and 6 or 4 and 8, and in order to make F a single-digit number, we can deduce that C = 2, E = 6 and F = 8.
So far, our number is AB2D68.
We know A + D = 8 so A and D are both odd numbers. The only odd number less than 8 that we can use for D to make one-quarter of two-digit number D6 also be a two-digit number is 7, so D = 7 and A is 1. This makes the two-digit number AB 19.
I change stature as I age, but my importance does not differ by age. My importance is manifested mostly when with my boss. When we part, I am of no importance.
A pencil. It gets shorter with use, but is no less important. Its impact is from the person using the pencil to write or draw. Without them, the pencil is just an idle tool.
Maya’s mother asked her to buy some stamps. The available stamps were 3 cents, 9 cents, 11 cents, 17 cents and 21 cents. Her mother asked her to buy eight each of three stamps and nine of each of the remaining two stamps. Unfortunately, Maya forgot which stamps she was supposed to buy eight and nine of. Luckily, her mother had given her $5, the exact amount required to buy the stamps. Which stamps did she buy?
Fred brings home 100 pounds of potatoes, which (being purely mathematical potatoes) consist of 99 percent water. He then leaves them outside overnight so that they consist of 98 percent water. What is their new weight?
100 lb of potatoes with 99% water weight means there’s 99 lb of water and 1 lb of solids, a 1:99 ratio.
If the water decreases to 98%, then the solids account for 2% of the weight. The 2:98 ratio reduces to 1:49. Since the solids still weigh 1 lb, the water must weigh 49 lb for a total of 50 lbs for the answer.
You’re in a build headed to the fourth floor. When you reach the second floor, you’ve gone one floor and have two more floors left, so you’re 1/3 of the way. But at the same time, you’re on the 2nd floor and have two more floors to get to the 4th floor, thus you’re halfway there.
This doesn’t work in Europe, because they typically refer to the “first floor” as the ground floor, and the first floor is one story up.
The name ABRAHAM can be changed into a word for a primitive musical instrument by replacing each letter with a different letter. The repeated letters (A is this case) must be replaced with the same replacement letter in the new word.
Mrs. Shine was having a rough day and wanted a break. So she asked her class to calculate the sum of the first 50 odd numbers. In a few moments, Winifred was at her desk with the correct answer of 2,500. Stunned, Mrs. Shine figured she must have gotten lucky, and sent precocious Winifred back to her seat with the task of finding the sum of the first 75 odd numbers. Again, Winifred returned in seconds with the correct answer (5,625).