DAY 404

What is unusual about the following sequence of numbers?

1, 4, 9, 6, 1, 5, 10, 4, 2

HINT:
It has to do with Roman Numerals.

Answer:

Written in Roman Numerals, these numbers form a palindrome. That is, they read the same in both directions.

I IV IX VI I V X IV II

DAY 403

Fred says to Jack, "I'll bet you $1 that if you give me $2, I'll give you back $3." Should Jack take the bet?

Answer:

No ........... If Jack takes the bet, he gives Fred $2. Fred can then say, "You win. I lose the bet." He then gives Jack $1 - the amount of the bet - but keeps Jack's other dollar.

DAY 402

If 3 cats can catch 3 mice in 3 minutes, how long would it take the 3 cats to catch 100 mice?

Answer:

102 minutes ........... If 3 cats can catch 3 mice in 3 minutes, it takes each cat 3 minutes to catch 1 mouse.

1 cat - 1 mouse - 3 minutes

3 cats - 3 mice - 3 minutes

3 cats - 6 mice - 6 minutes

3 cats - 9 mice - 9 minutes

.

.

.

.

3 cats 99 mice - 99 minutes

(Every 3 minutes, one mouse is caught by each cat. In 99 minutes, each cat catches 33 mice ........ 3 x 33 = 99)

To catch the 100th mouse takes another 3 minutes ........ 99 + 3 = 102 minutes

OR

100 mice/3 cats = 33 - the number of mice caught by each cat

( + remainder 1 mouse)

Since it takes 3 minutes for each cat to catch one mouse,

3 x 33 =99 minutes

+ 3 minutes to catch the remaining mouse = 102 minutes

DAY 401

10 ice cream bars and 6 ice cream cones cost $13.00.

6 ice cream bars and 10 ice cream cones cost $11.00.

How much for each ice cream bar and each cone?

Answer:

Ice cream bars cost $1.00, and cones cost $.50 .

16 bars and 16 cones cost $24.00 .

1 bar and 1 cone cost 24/16 = $1.50 .

DAY 400

Three children, Peter, Jane, and Eric share a bag of peanuts. There are 770 peanuts in the bag. For every 4 peanuts Peter took, Jane took 3. For every 6 peanuts Peter took, Eric took 7. How many peanuts did Peter get?

Answer:

264 ........... For every 12 peanuts Peter took, Jane took 9 and Eric took 14. This totals 35 peanuts for each round ... 770/35 = 22 rounds ... 12 x 22 = 264

DAY 399

360 doctors and nurses work in a hospital. If the ratio of doctors to nurses is 7 to 11, how many nurses are there?

Answer:

220 .......... 7 + 11 = 18. 360/18 = 20. There are 20 groups of doctors and nurses. If the ratio is 7 to 11, there are 7 x 20 = 140 doctors, and 11 x 20 = 220 nurses.

DAY 398

A postman delivers one letter on his first day of work, three letters on his second day of work, five letters on the third day, and so on - delivering two letters more each day than he delivered the previous day. How many total letters has he delivered after fifteen days of work?

Answer:

225

DAY ................ NUMBER OF LETTERS DELIVERED

1 .................................................... 1

2 ................................................... 3

3 ................................................... 5

4 ................................................... 7

5 ................................................... 9

6 .................................................. 11

The total number of letters delivered is the square of the number of days worked. For example, after 4 days, he has delivered 1 + 3 + 5 + 7 = 16 letters.