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MIND-Xpander Logic Puzzle

MIND-Xpander

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).

- DCCLXV – CXX + XLIV – XCV = ?
- CCCXXI + DCLIV + CMLIIIVII = ?
- DIII + XDXII + CMXXIV + CLXXI = ?
- 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 (?).

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### Last month's solutions

**MIND-Xpander** Maths Problem

**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)^{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**