The Missing Dollar

The initial payment of $30 is accounted for as the owner takes $25, the waiter takes $2, and the diners get a $3 refund. It adds up. After the refund has been applied, we only have to account for a payment of $27. Again, the owner keeps $25 and the waiter gets $2. This also adds up.

There is no reason to add the $2 and $27 – the $2 is contained within the $27 already. Thus the addition is meaningless. Instead the $2 should be subtracted from the $27 to get the revised bill of $25.

This becomes clearer when the initial and net payments are written as simple equations. The first equation shows what happened to the initial payment of $30:

$30 (initial payment) = $25 (to owner) + $2 (to waiter) + $3 (refund)

The second equation shows the net payment after the refund is applied (subtracted from both sides):

$27 (net payment) = $25 (to owner) + $2 (to waiter)

Both equations make sense, with equal totals on either side of the equal sign. The correct way to get the waiter's $2 and the guests $27 on the same side of the equal sign ("The waiter has $2, and the guests paid $27, how does that add up?") is to subtract, not add:

$27 (final payment) - $2 (to waiter) = $25 (to owner)

Puzzle

Puzzle for the chips question

20 blue chips

Puzzle of the Week

* 3 5 *
7 1 8 2
* 4 6 *

Puzzle of the Week (Harder than normal)

Stockbroker Mr. Get U. Rich calculates his profit % on cost price so his cost price is $1000/1.25= $800 and has thus made a profit of $200.

Stockbroker Mr. U. R. Clever has calculated his profit % on selling price, so his cost price should be $1000*(1-.25)= $ 750, hence his profit is $ 250, so in reality Stockbroker Mr. U. R. Rich has made more money for his client!

Tom and Jerry

Jerry beats Tom (Again!)
Jerry needs to run 6 meters, (added the extra second before the sofa), while Tom has to run 9.5 meters (added the seconds taken to wriggle out)
6/1 = 6 seconds
9.5/1.5 = 6 and 1/3 seconds.
Jerry will beat Tom by half a meter or 1/3 of a second to Jerry's hole.

Make 24

(10 x 10 - 4)/4

Make 24

8 5 4 10 = 24

(8+4)x (10/5)

2 8 5 5

(5/5+2)x8

6 6 8 4

(6+6)x (8/4)

1 3 10 4

(3-1)x (10+4)

13 8 2 6

13 x (8-6) - 2

10 3 8 9

8 x 3 x 10 -9

Puzzle of the Week

123 -45-67+89=100

Hmmm A Few More Puzzles

1. The last person took the basket with the egg in it.

2. All the others were women

3. Pour the juice from the 2nd glass to the 5th

4. The recluse lived in a lighthouse

Puzzle

He needs to take 1 bolt from crate 1
2 bolts from crate 2
3 bolts from crate 3
4 bolts from crate 4
5 bolts from crate 5
and weigh them altogether.
If he gets 5 g overweight he knows it is crate 5 etc

Puzzle Year 6 Year 7

19/95 25/65 16/64

Can all be reduced by cancelling the number that is common in the denominator and numerator

Make 24

4 7 8 8

(7 - 8/8) X 4

There were many answers to this one!

Year 6 Puzzle

Start with a 6 digit number that begins with 1. Move the 1 from the hundred thousands place to the digits place. The number is now 3 times bigger than the original number. (The other digits stay exactly the same)


The first number can be expressed as
100 000 +x
The second number can be expressed as
10x +1

3(100 000 + x) = 10x +1
300 000 + 3x = 10x + 1
299 999 = 7x
42857

142857

Puzzle

Mr Golan asked the class to see if they could find the sum of the first 50 odd numbers. As everyone settled down to their addition, Julia ran to him and said, "The sum is 2,500." Mr Golan thought, "Lucky guess," and gave him the task of finding the sum of the first 75 odd numbers. Within 20 seconds, Julia was back with the correct answer of 5,625.
How did she do this?

Actually all you have to do is square the number of odd numbers you want added ie

The sum of the first 50 odd numbers is 50^2 (50 squared)

The sum of the first 75 odd numbers is 75^2 (75 squared)

Answer to 2nd Make 24 puzzle

1 3 4 6 = 24

6 / (1 -3/4)
6 divided by 1 - three quarters

Answer to 1st Make 24 Puzzle

With 3 3 7 7 make 24

(3+3/7) x 7