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Each month, a new set of puzzles will be posted.  Come back next month for the solutions and a new set of puzzles, or subscribe to have them sent directly to you.

Arith-Maze

In the following numeric-maze, go to the ‘START’ box and proceed through the maze, following instructions as provided, until you get to the ‘FINISH’ box. What number did you finish with?

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Last month's solutions

Puzzle One

On the clock below, the time shown is 14:23:30. Can you determine the exact angle, in degrees, that the hour and minute hands make at this time?


Solution:  The angle is 141⁰ – 71.75⁰ = 69.25⁰

Puzzle Two

Under his new contract, Murray’s annual salary will increase by 4,000 each year after the 1st year. If his total annual salary projected over next 12 years is $1,266,580, and on his 10th year he is to receive a special bonus of 10% on his annual salary. What is his annual starting salary and also what is his projected salary for 12th year?

Solution:

Let x = his starting annual salary

Annual Salaries projection:

1st year = x
2nd year = x + 4,000
3rd year = x + 8,000
4th year = x + 12,000
5th year = x + 16,000
6th year = x + 20,000
7th year = x + 24,000
8th year = x + 28,000
9th year = x + 32,000
10th year =(x + 36.000 + 0.10 (x + 36,000) = 1.10x + 39,600
11th year = (1.10x + 39,600) + 4,000 = 1.10x + 43,600
12th year = (1.10x + 43,600) + 4,000 = 1.10x + 47,600

Total of 12 years of annual salaries:

12.3x + 914,800 = 1,266,580; 12.3x = 1,266,580 – 914,800 = 351,780

Therefore, x = 351,780 / 12.3 = $28,600 (Starting annual salary) and
And on the 12th year, 1.10x + 47,600 = (1.1 * 28,600) + 47,600 = 31,460 + 47,600 = 79,060.

Puzzle Three

What is the sum of 1+11+111+1111+11111+111111………up to 100 digits of 1?

Solution:

RULE for adding consecutive numbers in a group:
ADD the smallest number in the consecutive group to the largest,
MULTIPLY the result by the total numbers in the group, then
DIVIDE the product by 2;  i.e., [(1 +100) * 100] / 2 = 10100 / 2 =  5050

 

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