Tuesday 30 July 2013

DAY 414

Farmer Fred had sixteen chickens. A fox killed all but six of them. How many chickens does Farmer  Fred have left?

Answer:

Six

Sunday 21 July 2013

DAY 413
Credit: NPR Car Talk Puzzler
June 29, 2013

Tom and Ray, the Car Talk brothers, go out to eat with a group of friends. When the bill comes, the two brothers go to the bathroom and climb out the window. Realizing they've  been stiffed, the remaining group looks at the bill, which is $63. One of them correctly says, "If each of us chips in an extra two dollars, we'll have it covered."  How many were in the original group (i.e. including Tom and Ray)?

Answer:

Nine ............. The only two factors of 63 with a difference of two are 7 and 9. If Tom and Ray had paid their share, each of the nine people would have paid $7. Now, each of the remaining
seven people have to pay $9 each - a difference of $2.

Saturday 20 July 2013

DAY 412

A fruit seller has a basket of oranges. His first customer buys half the oranges plus half an orange. The next customer buys half of what's left plus half an orange. The last customer buys half of what's left plus half an orange, leaving the basket empty. No oranges were cut or broken in any way. How many oranges did the fruit seller start with?

Answer:

Problems like these can be solved with algebra, but a simpler solution is possible. Since the problem tells us no oranges were cut or broken, we know that only whole oranges were sold to the customers. The "half" orange must be used to complete a whole orange - as in 1 1/2 + 1/2 = 2. The only way to take half of a number and add 1/2 to it to get a whole number, is to start with an odd number. 

In this problem, since there were only three transactions before the basket was emptied, there could not have been that many oranges. Thinking of the odd numbers - 1, 3, 5, 7, 9, 11 ............... 7 oranges solves the problem:

First customer: 3 1/2 (half of seven) + 1/2 = 4 (leaving 3)
Second customer: 1 1/2 (half of three) + 1/2 = 2 (leaving 1)
Third customer: 1/2 (half of one) + 1/2 = 1 (leaving 0)

DAY 411

Instead of buying 4 hamburgers and 3 drinks for $14.50, Ralph buys 3 hamburgers and 4 drinks for $13.50. What is the price of each hamburger and each drink?

Answer:

Each hamburger is $2.50 and each drink is $1.50.

7 hamburgers and 7 drinks would cost $28.00.
1 hamburger and 1 drink cost $28.00/7 = $4.00.


 
DAY 410

The four numbers below are perfect squares. What else is unusual about them?

25
100
169
225

Answer:

Each number can be expressed as the sum of two other perfect squares:

25 = 9 + 16
100 = 36 + 64
169 = 144 + 25
225 = 144 + 81

Sunday 14 July 2013

DAY 409

WHAT'S NEXT?
Credit: Will Shortz
NPR Weekend Edition Sunday Puzzle

What is the next number in this series?

2, 4, 6, 9, 11, 15, 20, 40, 51, 55, 60, 90, ???

Answer:

101 ............... Each number can be expressed in Roman Numerals by two digits:

II, IV, VI, IX, XI, XV, XX, XL, LI, LX, XC, CI