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Donald Cartmill

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About Donald Cartmill

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  1. Adapting a classic crossing puzzle

    9 minutes; i.e. 1 rower & 2 non rowers cross in 4 minutes ; 1 rower returns in 1 minute ; 2 rowers and 1 non rower cross in 4 minutes.
  2. Soldiers in a field

  3. Whodunit?

  4. Soldiers in a field

    Not exactly a proof ,but if all soldiers watch the soldier to their left, then the soldier to the extreme right is NOT being watched. and the reverse is true. Taking the smallest odd number 3, if the middle man looks left then the man on the right is not watched . The only way all ARE watched is if they are in a circle.
  5. Distance between nails

  6. Colored hats, revisited

  7. 3 = 4 + 5 - 6 ; 5 - 4 + 5 = 6 ; 3 - 4 + 6 = 5
  8. How much white?

    Area of the white is = 1 (1/4) + 9(1/4 x 1/4 ) + 27 ( 1/4 x 1/4 x 1/4) + 81 ( 1/4 x 1/4 x 1/4 x 1/4 ) The lowest common multiple of all of the divisors is 1024 or 4 x 4 x 4 x 4 Area of the white is = 256/1024 + 192 / 1024 +144/1024 +108/1024 + 81/1024; Totaling these =781 / 1024 then dividing 1024 into 781 you get 0,762695313 rounding off to 3 places = 0.763
  9. How much white?

    Area of white to 3 places is = 0.763
  10. Move the matchstick

    remove 1 match from the 6 making it a 5 ; Then place the match horizontally to the top of the 1 ,making it a 7; 5 + 7 + 13
  11. 3-color cube

  12. 3-color cube

  13. How many squares?

    Tried to edit my previous answer and lost everything . Correction ...Red sq "beneath "gray and rotated 60 degrees; Red sq "a top" gray sq and rotated 30 degrees new answer is 8 ; 1 beneath the gray but rotated 60 degrees ,a 2nd above the gray but rotated 30 degrees.4 more one at each corner= 6 ,however if you rotate the top two corner reds away from center you can place a red with one corner touching the gray at the mid point of the top side of the gray. You can do the same at the bottom two corner "Reds",rotating them outward and then placing the 8th red with a corner touching the gray at the midpoint of the grays' bottom side. If the red over gray is considered to be touching the red beneath the gray then the answer is 7
  14. How many squares?

    Captain Ed had the answer a red beneath the gray but rotated 60 degrees; another red a top of gray and rotated 30 degrees. Then you have one red at each of the four corners,which totals 6 new answer is 8 ; 1 beneath the gray but rotated 60 degrees ,a 2nd beneath the gray but rotated 30 degrees.4 more one at each corner= 6 ,however if you rotate the top two corner reds away from center you can place a red with one corner touching the gray at the mid point of the top side of the gray. You can do the same at the bottom two corner "Reds",rotating them outward and then placing the 8th red with a corner touching the gray at the midpoint of the grays' bottom side. If the red over gray is considered to be touching the red beneath the gray then the answer is 7
  15. Stefan borrowed a watch from his friend ,returned home and set his grandfather clock to the correct time

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