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Donald Cartmill

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  1. Donald Cartmill

    20 RIDDLES TO TEST YOUR MATH, IQ AND THINKING SKILLS.

    . What is the value of x If 1/2, 2/3, 3/4, 4/5, 5/6, 6/7, 7/8, 8/9, 9/10 then x/1000? x = 500,000 CORRECTION x =900 2. If 4 and 2= 26, 8 and 1 = 79 and 6 and 5 = 111. Then, what is 7and3?...410 3. What 3 positive numbers give the same result when multiplied and added together? 2 mis interpreted the Q 1,2,3 is correct 4. What number do you get when you multiply all of the numbers on a telephone's number pad? zero 5. Here is a light switch. Note the order of the positions. If the light is now at medium and it is switched 3922 times what will be the position of the switch? medium I assumed in the absence of additional info there were 3 positions . i.e low , med , high. any even number of flips will put the sw back on med 6. Can you arrange four nines to make it equal to 100. 99 9/9 8. If 1/2 of 5 is 3, then what is 1/3 of 10? 3.67 I envisioned 1/2 of 5 = 2 1/2 + 1/2 = 3; therefore 1/3 of 10 = 3.33 + 1/3 =3.367 9. 100 students entered college. 55 of them chose music. 44 of them chose sports. 20 of them chose both. How many of them chose neither music nor sports? 21 Of the 55 ,20 choose both leaving 35 ; of the 44 ,20 choose both leaving 24; 35 music only ;24 sports only ; 20 M&S total=79 100 - 79 = 21 who do neither 10. Four friends are going to a concert. When they arrive, there are only five seats together left in the theater. The manager will let all four friends in for free if one of them can tell her how many different seating arrangements are possible for four people with five empty seats. 120 5 seats taken 4 at a time 5 ! All four are let in free. Could you have given the correct answer? 120 5 seats taken 4 at a time 5 ! 12. At six o’clock the wall clock struck 6 times. Checking with my watch, I noticed that the time between the first and last strokes was 30 seconds. How long will the clock take to strike 12 at midnight? 5 hrs 59 1/2 minutes NOTE: the question is not how long it chimes at 12 :00 ,but how long from the 30 seconds of chiming at 6:00 3. There are several books on a bookshelf. If one book is the 4th from the left and 6th from the right, how many books are on the shelf? 9 14. John has been hired to paint the numbers 1 through 100 on 100 apartments. my bad 20 How many times he has to paint 8? 20 15. You have two books. One of them is upside-down and the other is rotated so the top of the book is facing you. What is the sum of the first page in each book? 1 +1 Up side down ,laying on its side ,propped at an angle the first page is 1 16. There is a certain club which is for men only. There are 600 men who belong to this club and 5% of these men wear one earring. Of the other 95% membership, half wear two earrings and the other half wear none. How many earrings are being worn in this club? 600 17. Does a pound of gold or a pound of feathers weight more? feathers A pound of feathers weighs 16 ounces avoirdupois; Gold is weighed on the troy system whereby a troy pound is 12 oz ; 1 troy oz = 1.0971 oz avoirdupois therefore 1 pound of gold weighs 13.1652 oz avoirdupois 18. There is a chain nailed to the wall. The chain is 10 feet long and the center of the chain dips down 5 feet from where each side of the chain is nailed to the wall. How far are the 2 ends of chain from each other? on the same nail 19.Little Johnny is walking home. He has $300 he has to bring home to his mom. While he is walking a man stops him and gives him a chance to double his money. The man says "I'll give you $600 if you can roll 1 die and get a 4 or above, you can roll 2 dice and get a 5 or 6 on at least one of them, or you can roll 3 dice and get a 6 on at least on die. If you don't I get your $300." What does Johnny do to have the best chance of getting home with the money? keep on walking 20. If you have 6 women and 2 friends, how many women do each of your friends get if the friends are two of the 6 women;i.e. women themselves , then each is entitled to herself, or one each/ If the two friends are male then no women.
  2. Donald Cartmill

    20 RIDDLES TO TEST YOUR MATH, IQ AND THINKING SKILLS.

    . What is the value of x If 1/2, 2/3, 3/4, 4/5, 5/6, 6/7, 7/8, 8/9, 9/10 then x/1000? x = 500,000 2. If 4 and 2= 26, 8 and 1 = 79 and 6 and 5 = 111. Then, what is 7and3?...410 3. What 3 positive numbers give the same result when multiplied and added together? 2 mis interpreted the Q 1,2,3 is correct 4. What number do you get when you multiply all of the numbers on a telephone's number pad? zero 5. Here is a light switch. Note the order of the positions. If the light is now at medium and it is switched 3922 times what will be the position of the switch? medium I assumed in the absence of additional info there were 3 positions . i.e low , med , high. any even number of flips will put the sw back on med 6. Can you arrange four nines to make it equal to 100. 99 9/9 8. If 1/2 of 5 is 3, then what is 1/3 of 10? 3.67 I envisioned 1/2 of 5 = 2 1/2 + 1/2 = 3; therefore 1/3 of 10 = 3.33 + 1/3 =3.367 9. 100 students entered college. 55 of them chose music. 44 of them chose sports. 20 of them chose both. How many of them chose neither music nor sports? 21 10. Four friends are going to a concert. When they arrive, there are only five seats together left in the theater. The manager will let all four friends in for free if one of them can tell her how many different seating arrangements are possible for four people with five empty seats. 120 5 seats taken 4 at a time 5 ! All four are let in free. Could you have given the correct answer? 120 5 seats taken 4 at a time 5 ! 12. At six o’clock the wall clock struck 6 times. Checking with my watch, I noticed that the time between the first and last strokes was 30 seconds. How long will the clock take to strike 12 at midnight? 5 hrs 59 1/2 minutes 13. There are several books on a bookshelf. If one book is the 4th from the left and 6th from the right, how many books are on the shelf? 9 14. John has been hired to paint the numbers 1 through 100 on 100 apartments. my bad 20 How many times he has to paint 8? 20 15. You have two books. One of them is upside-down and the other is rotated so the top of the book is facing you. What is the sum of the first page in each book? 1 +1 16. There is a certain club which is for men only. There are 600 men who belong to this club and 5% of these men wear one earring. Of the other 95% membership, half wear two earrings and the other half wear none. How many earrings are being worn in this club? 600 17. Does a pound of gold or a pound of feathers weight more? feathers 18. There is a chain nailed to the wall. The chain is 10 feet long and the center of the chain dips down 5 feet from where each side of the chain is nailed to the wall. How far are the 2 ends of chain from each other? on the same nail 19.Little Johnny is walking home. He has $300 he has to bring home to his mom. While he is walking a man stops him and gives him a chance to double his money. The man says "I'll give you $600 if you can roll 1 die and get a 4 or above, you can roll 2 dice and get a 5 or 6 on at least one of them, or you can roll 3 dice and get a 6 on at least on die. If you don't I get your $300." What does Johnny do to have the best chance of getting home with the money? keep on walking 20. If you have 6 women and 2 friends, how many women do each of your friends get if the friends are two of the 6 women;i.e. women themselves , then each is entitled to herself, or one each/ If the two friends are male then no women.
  3. Donald Cartmill

    20 RIDDLES TO TEST YOUR MATH, IQ AND THINKING SKILLS.

    . What is the value of x If 1/2, 2/3, 3/4, 4/5, 5/6, 6/7, 7/8, 8/9, 9/10 then x/1000? x = 500,000 2. If 4 and 2= 26, 8 and 1 = 79 and 6 and 5 = 111. Then, what is 7and3?...410 3. What 3 positive numbers give the same result when multiplied and added together? 2 4. What number do you get when you multiply all of the numbers on a telephone's number pad? zero 5. Here is a light switch. Note the order of the positions. If the light is now at medium and it is switched 3922 times what will be the position of the switch? medium 6. Can you arrange four nines to make it equal to 100. 99 9/9 8. If 1/2 of 5 is 3, then what is 1/3 of 10? 3.67 9. 100 students entered college. 55 of them chose music. 44 of them chose sports. 20 of them chose both. How many of them chose neither music nor sports? 21 10. Four friends are going to a concert. When they arrive, there are only five seats together left in the theater. The manager will let all four friends in for free if one of them can tell her how many different seating arrangements are possible for four people with five empty seats. 240 All four are let in free. Could you have given the correct answer? 240 12. At six o’clock the wall clock struck 6 times. Checking with my watch, I noticed that the time between the first and last strokes was 30 seconds. How long will the clock take to strike 12 at midnight? 5 hrs 59 1/2 minutes 13. There are several books on a bookshelf. If one book is the 4th from the left and 6th from the right, how many books are on the shelf? 9 14. John has been hired to paint the numbers 1 through 100 on 100 apartments. 11 How many times he has to paint 8? 11 15. You have two books. One of them is upside-down and the other is rotated so the top of the book is facing you. What is the sum of the first page in each book? 1 +1 16. There is a certain club which is for men only. There are 600 men who belong to this club and 5% of these men wear one earring. Of the other 95% membership, half wear two earrings and the other half wear none. How many earrings are being worn in this club? 600 17. Does a pound of gold or a pound of feathers weight more? feathers 18. There is a chain nailed to the wall. The chain is 10 feet long and the center of the chain dips down 5 feet from where each side of the chain is nailed to the wall. How far are the 2 ends of chain from each other? on the same nail 19.Little Johnny is walking home. He has $300 he has to bring home to his mom. While he is walking a man stops him and gives him a chance to double his money. The man says "I'll give you $600 if you can roll 1 die and get a 4 or above, you can roll 2 dice and get a 5 or 6 on at least one of them, or you can roll 3 dice and get a 6 on at least on die. If you don't I get your $300." What does Johnny do to have the best chance of getting home with the money? keep on walking 20. If you have 6 women and 2 friends, how many women do each of your friends get if the friends are two of the 6 women;i.e. women themselves , then each is entitled to herself, or one each/ If the two friends are male then no women.
  4. Donald Cartmill

    You're super genius if you solve this Puzzle

    90 students however there are 95 involvements i.e. ( 30 fb; 40 vb; 25 bb ). That there are 23 who do not participate is NOT crucial to the solution. A ) 15 fb + vb ; B) 10 fb + bb ; C) 8 bb + vb ;; 15 fb+ 10 fb =25 fb combined plus 5 ; 15 vb + 8 vb = 23 vb plus 17 ; 10 bb + 8 bb = 18 bb plus 7 The plus 5 ; plus 17; plus 7 represents respectively those who play only 1 or all 3 sports . = 29 Now 25 + 23 + 18 = 66 involvements; plus 29 involvements = 95 involvements Therefore the plus 5 ; plus 17; plus 7 represents respectively those who play only 1 sport and there were none who played all 3 sports I yield to Rubaidi's Venn diagram above great solution
  5. Donald Cartmill

    Brainden races

    While the combined speed ratios provide the correct answer . I still maintain the speed ratio of A to B is not crucial to the solution. i.e. Let us suppose that A is merely to step out at the finish line to congratulate B and C the competitors in a two man race . A steps out when B has run 80 meters; Congratulates B when B completes the race and notes at the time C has completed 80 meters. Where was C when A first made his appearance ? The answer is 4/5 x 80 = 64 meters While the combined speed ratios provide the correct answer . I still maintain the speed ratio of A to B is not crucial to the solution. i.e. Let us suppose that A is merely to step out at the finish line to congratulate B and C the competitors in a two man race . A steps out when B has run 80 meters; Congratulates B when B completes the race and notes at the time C has completed 80 meters. Where was C when A first made his appearance ? The answer is 4/5 x 80 = 64 meters To beat a dead horse let A step out when B is at 85 meters; He then congratulates B as he finishes the race and notes C is at 80 meters. He wonders where was C , when I first stepped out ??? The answer is of course 4/5 x 85 = 68 meters
  6. Donald Cartmill

    Brainden races

    Yes ,I agree Capt Eds' answer is not quite as straight forward as could be. After A reaches 100 m ...20 m ahead of B , the speed of A is not significant to the solution. The key is that when B is at 100 ,C is at 80. Therefore C is 8/10 the speed of B and it follows that when B was at 80 m...C was at 8/10 x 80 = 64 m. A is at 100 m when C is at 64 therefore A beats C by 36 m
  7. Donald Cartmill

    Brainden races

    A crosses finish 20 meters a head of B ; Now B crosses 20 meters ahead of C ; i.e. B at 100 meters ...C at 80 meters; therefore C was traveling at 8/10 the speed of B. Therefore when B was at 80 meters ...C was 8/10 x 80 meters or 64 meters. Thus A beat C by 36 meters
  8. Donald Cartmill

    Strange math problem

    The answer given is 5! , which closely resembles 51 or 5 ! exclamation mark. It is however 5 factorial or 5 x 4 x 3 x 2 x 1= 120 25 - 55 + ( 85 + 65 ) = 120 =5 ! 25 - 55 + (150 ) ; -55 + 175 ; 175 - 55 == 120
  9. Donald Cartmill

    Poisonous apples

    the odds of eating a poison apple for the 1st bowl = 3/5 + 3/4 = 12/20 + 15/20 = 27/20 = !.35 chances of eating the P/A 2nd bowl =2/5 + 2/4= 2/3 = 24 /60 +30/60 + 40/60 = 84/60 = 1.4 CHANCES Therefore you would eat from the 1st bowl with a 0.05 better chance of avoiding the P?A
  10. Donald Cartmill

    Line segments of two types

    I'm not sure I recognize your solution 6 from its description of how it's constructed, but your final description of it seems right. Nice solve. Let me attempt to clarify 6) 4 points A,B,C,D, lay on two intersecting circles having the same radius. point A is the center of one circle with C and D laying on its circumference , D is the center of the 2nd circle with A and B laying on its circumference. The 4 points create a trapezoid in which The diagonals AC , & BD plus the base AD are equal all being a radius. Points B and C lay on their respective circumferences at points where the chords AB = CD = equals the top BC I don't know if that is any more clear
  11. Donald Cartmill

    Balancing weights

    4 would be the smallest number. assign a unit weight of 1 ;2 ;3 ;4; to the 4 weights place units 1 and 4 on left pan and 2 and 3 on the right pan each weigh 5 and balance sorry I misunderstood the question in my earlier answer
  12. Donald Cartmill

    The holy mans walk up the mountain

    Two of you got the answer ,but seemingly struggled with the simplicity of the solution. i.e. If a second man started up the mountain at the same time the other was coming down...regardless of their relative speeds ,stopping to rest , at some point they must meet , and obviously at the same time.
  13. Donald Cartmill

    The holy mans walk up the mountain

    A holy man starts up a mountain at 7:00 am ; Arrives at the top at 7:00 pm He goes thru some worship ceremony and the next morning ,and the next morning at 7:00 am he starts back down the mountain. He arrives at the bottom at 7:00 pm . Is there a place where going up and coming down he was at the place at the same time both days. Proof please
  14. Donald Cartmill

    Staying dry in the rain

    First thought is that no matter how fast Albert runs his front always sees 2000 rain drops. i.e. his front is 2 square meters and he is seeing 1000 drops/cu meter . On the other hand the top of Albert 0.20 square meters. if Albert was 1 sq meter, moving at 1 m/sec ,then his top sees ( 1,000 / cu meter falling at 10 m/sec = 10,000 drops) however ,Albert has only a 0.20 sq meter profile therefore his top would see ( 10,000 x 0.20 = 2,000 drops ) if he moves at 2 meters / sec then he is hit on top by 1,000 drops. if then he is moving at 4 m/sec 2,000 divided by 4 = 500 drops. There fore Albert should run as fast as possible
  15. Donald Cartmill

    Staying dry in the rain

    First thought is that no matter how fast Albert runs his front always sees 2000 rain drops. i.e. his front is 2 square meters and he is seeing 1000 drops/cu meter . On the other hand the top of Albert 0.20 square meters. if Albert was 1 sq meter moving at 1 m/sec ,then his top sees ( 1,000 / cu meter falling at 10 m/sec = 10,000 drops ) however his profile is only 0,20 sq meters and therefore he sees ( 0.20 x 10,000 drops = 2,000 drops ); If he moves at 2 m/sec ; then he sees 1,000 drops at 4 m/sec he would see 500 drops,etc So Albert should run as fast as possible.
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