32. A, B, C, D, E, and F are sitting on six chairs placed around a round table, not necessarily in that order. A is between D and F. C is opposite D and D and E are not sitting next to each other. Which of these pairs are sitting next to each other?
(i) A and B (ii) C and E (iii) B and F (iv) A and C
4d - 2o = 10a + b
4d - 3o = 10b + a ( a and b are arbitrary numbers between 1 and 9 inclusive)
Quite a lot of this cancels out, leaving o = 9(a-b).
(If o=9 then a-b=1, a>b; o<=d/2)
I came up with almost the same equations but yours are neater (using d instead of r) so I quote yours, hope you don't mind Mathsyperson.
I tried to cancel o out, leaving 4d=28a-17b
4d is even so 17b must be even or b even.
d, a, b are integers and d>0, a>0, b>0, a<>b
Replace a, b with value 1..9 or 2..8 and I have d=18; 8; 32; 46 mm
d=8 too small, d=46 too big a coin, that left d=18 mm (a=5, b=4) or 32 mm (a=7, b=4).
But it looks like only d=18 mm works.
What's wrong with my solution ?
28) I get 44 times at right angles. I was too lazy, I only counted 22 from 6am to 6pm.
What is the answer for a seven-hour clock and a fourteen hour day?? Do you know Ganesh? I don't.
The reason I ask is because with a 12 hour clock the 9 and the 3 are at right angles to the 12 at the top, so
the answer is less than 12 x 2 for 12 hours, but a seven hour clock would be weird, or a 5 hour clock too.
Hmmm.... I'll have to ponder this more later...
And I only see 42 times accounted for! I must have lost count around the dial.
#43. What goes up and down the stairs without moving?
#47. What goes around the world but stays in a corner?
#49. Give me food, and I will live; give me water, and I will die. What am I?
#54. No sooner spoken than broken. What is it?
#55. A certain crime is punishable if attempted but not punishable if committed. What is it?
#59. I went into the woods and got it. I sat down to seek it. I brought it home with me because I couldn't find it. What is it?
18. A woman goes into a hardware store to buy something for her house. When asked the price, the clerk replies, "the price of one is twelve cents, the price of forty-four is twenty-four cents, and the price a hundred and forty-four is thirty-six cents. What does the woman want to buy?
Let 1,2,3 be the 1st, 2nd, 3rd soldier.
Case 1: R R B (1 and 2 wearing red cap and 3 wearing blue cap)
3 would have found out that he was wearing blue cap. But he couldnt tell so this is not correct order .
Case 2: R ? ?
2 would have known that he was wearing blue cap because if he was wearing red cap (case 1) then 3 figured out answer already.
But 2 couldnt answer so 1 must be not wearing red cap.
Case 3: B ? ?
2,3 wouldnt have enough facts to figure out the color of their caps.
1 considers case 1 and case 2 then he figures his cap is blue.