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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.

## MIND-Xpander Logic Puzzle

There are five people in a room and each shakes every other person’s hand exactly one time. How many handshakes will there be?

## Roman Arithmetic Puzzles

Solve the following arithmetic problems and state your answers in Roman Numerals.  Letters representing numbers in the Roman numerical system: I = 1, V = 5, X = 10, L = 50, C = 100, D = 500, M = 1,000. In this system, a letter placed after another of greater value adds (thus XVI is 16) whereas a letter placed before another of greater value subtracts (thus XC is 90).

1. DCCLXV – CXX + XLIV – XCV = ?
2. CCCXXI + DCLIV + CMLIIIVII = ?
3. DIII + XDXII + CMXXIV + CLXXI = ?
4. DCLXVI – DVI + DLV + CCCXXXIII + CDXLIV = ?

## HEXAGON-numeric Puzzle (Level 2)

Fit the numbers 1 – 6 in each hexagon and where the hexagon segments touch each other, their numbers in these 2 segments will be the same. No number can be repeated in a hexagon. The numbers in the shaded areas are the sum of the numbers in the 2 or 4 segments that they side with.  The numbers in the ‘Input’ and ‘Output’ boxes are the sum of the numbers in the 3 triangular segments that they side with. Solve the puzzle and find the ‘Output’ number (?). ## Feedback

There are more than one way of doing these puzzles and may well be more than one answer.  Please let me and others know what alternatives you find by commenting below.  We also welcome general comments on the subject and any feedback you'd like to give.

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## MIND-Xpander Maths Problem

1. The second of five consecutive multiples of 11 is removed. The other four are then added together to give 715. What is the lowest multiple of the remaining four?

There are two solutions.

Solution 1

Let x be the unknown multiplier to the multiples.

11x + 0 + 33x + 44x + 55x = 715

143x = 715

x = 5

Checking: 55 + 0 + 165 + 220 + 275 = 715

Solution 2

Let x be the lowest multiple multiplier.

11(x) + 0 + 11(x+2) + 11(x+3) + 11(x+4) = 715

11x + 0 + (11x + 22) + (11x + 33) + (11x + 44) = 715

44x + 99 = 715

44x = 616

x = 14

Checking: 154 + 0 + 176 + 187 + 198 = 715

2. Simplify this expression

√6  x  √15  x  √10

Solution

(√2  x  √3)  x  (√3  x  √5)  x  (√2  x  √5)   =   (√2) x   (√3)2  x   (√5)2

=  2   x   3   x  5  = 30

## PRIME Numbers Puzzle

Throwing 3 darts at the following dartboard and all 3 throws must hit a number on the dartboard, what are your chances that their total will equal a Prime Number?  Numbers can be used more than once. Solution

1-in-27 There are 3 possible combinations for each of the 3 darts or 27 (3³) different, equally likely combinations. The only combination that gives you a Prime Number is 1+1+1 = 3. All other combinations are divisible by 3.

## HEXAGON-numeric puzzle (Level 1)

Fit the numbers 1 – 6 in each hexagon and where the hexagon segments touch each other, the numbers in these segments will be the same. No number can be repeated in a hexagon. Find the remaining missing numbers to complete the following puzzle.

Solution 