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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.

HEXAGON-numeric Puzzle (Level 1)

Fit the numbers 1 to 6 in each hexagon so that where a hexagon touches another, the numbers in each of their touching segments are the same. No number is repeated in any hexagon. Solve the puzzle by finding all the missing numbers.

HEXAGON-numeric Puzzle (Level 2)

Fit the numbers 1 to 6 in each hexagon so that where a hexagon touches another, the numbers in each of their touching segments are the same.

  • No number is repeated in any 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 segments that they side with.

Solve the puzzle by finding the Output number.

HEXAGON-numeric Puzzle (Level 3)

Fit the numbers 1 to 6 in each hexagon so that where a hexagon touches another, the numbers in each of their touching segments are the same.

  • No number is repeated in any 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 Sum boxes are the sum of the numbers in the 4 segments that they side with.
  • The numbers in the Input and Output boxes are the sum of the numbers in the 3 segments that they side with.

Solve the puzzle by finding 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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Last month's solutions

Puzzle One

62 people have taken part in a survey on modes of transport they use to travel to work. They have been asked whether they travel by Car, Train and Bus only or a combination of these three modes of travel.

    • Twice as many people use the Car only as use the Car and Train.
    • Four more people use the Bus only than the Train only.
    • Twice as many people use the Train and Bus as use all three modes.
    • The same number of people use the Car and Bus as use the Bus only.
    • Thirteen more people use the Car only than the Bus only.
    • Two people use all three modes of transport.
    1. How many people travel by Car only?
    2. How many people travel by Train only?
    3. How many people travel by Bus only?
    4. How many people travel by Car and Bus?

Solution

Let: C = people travel by Car only
T = people travel by Train only
B = people travel by Bus only
(C + T) = people travel by Car & Train
(T + B) = people travel by Train & Bus
(C + B) = people travel by Car & Bus
(C + T + B) = people travel by all 3 modes

Given: C = 2 * (C + T)
B = (T + 4)
(T + B) = 2 * (C + T + B)
(C + B) = B
C = (B + 13)
(C + T + B) = 2,
Then, (T + B) = 2 * 2 = 4

P = Participants = 62 people = C + T + B + (C + T) + (T + B) + (C + B) + (C + T + B)
C + T + B + (C + T) + (T + B) + (C + B) + (C + T + B) = 62

(B + 13) + (B – 4) + B + C/2 + 4 + B + 2 = 62

4B + C/2 + 15 = 62

4B + (B + 13)/2 + 15 = 62, 4.5 B = 62 – 21.5 = 40.5, B = 9,

Then, T = (B – 4) = 5, C = (B + 13) = 22

And (C + T) = C/2 = 22/2 = 11

Puzzle Two

Find the number equivalent for the following alphametic expressions to make the equations true. Each letter is unique with values from 0 to 9. Note: There may be more than one solution.

    1. ZERO + ONE + TWO = THREE
    2. TWO + THREE + SEVEN = TWELVE
    3. THREE + THREE + ONE = SEVEN
    4. SEVEN + SEVEN + SIX = TWENTY

Solutions:

  1. 9635 + 546 + 185 =10366 &
    9635 + 586 + 145 =10366
  2. 106 + 19722 + 82524 = 102352 &
    104 + 19722 + 82526 = 102352
  3. 18299 + 18299 + 479 = 37077
  4. 68782 + 68782 + 650 = 138214

     

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