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.
Puzzle OneOn 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?
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Puzzle TwoUnder 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? |
Puzzle ThreeWhat is the sum of 1+11+111+1111+11111+111111………up to 100 digits of 1? |
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Last month's solutions
Puzzle OneTwo poles are shown in the diagram below with a guide wire stretched from the top of each pole to the base of the other. Their heights are 4.5 and 6 metres, and the wires cross at a height h (as shown). What is this height? Solution:
h/4.5 = b/(a + b), h = 4.5b/(a + b) (eq. 2) Since eq.1 = eq. 2, 6a/(a + b) = 4.5b/(a + b) By cross multiplication, 6a/4.5b = (a + b) / (a + b) = 1 and a/b = 4.5/6.0 = ¾ and b/a = 4/3 And dividing both the numerator and denominator of eq.1 by ‘a’, then: h = 6a/(a + b) = (6 a/a) / ((a + b)/a) = 6 / (1 + b/a) = 6 / (1 + 4/3) = 6 / (7/3) = 18/7
To check eq.1’s answer, dividing the numerator and denominator of eq. 2 by ‘b’ then: h = 4.5b/(a + b) = 4.5b / (a/b + 1) = 4.5 / (1 + 3/4) = 4.5 / (7/4) = 18/7 = 2.57m (approx.) |
Puzzle TwoIn the numeric jungle below, can you find a path from IN to OUT by avoiding all multiples of 6 squares? (Note: You can also travel diagonally if required.) Solution:
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Puzzle ThreeIn the diagram below, the equilateral triangle is divided into two identical equilateral triangles A and C, and two parallelograms B and D which are mirror images of each other. What is the ratio of area D to area A ? Solution:
If you divide the two equilaterals and parallelograms in half as shown by the red dash lines, there are now 8 identical triangles. Of these 8 identical sized triangles, D contains 2 and A also contains 2, therefore the ratio of area D to area A is equal 2 to 2 or 1 to 1 (1:1). |
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