Solutions to the twists For your entertainment only and thanks for support. all puzzles

(1)

 Turn on switch 1 for a while and turn it off. Turn on switch 2. Go to the other room. The bulb that is off but feels warm is controlled by switch 1. The bulb that is on is controlled by switch 2. The remaining bulb is controlled by switch 3. back to puzzle

(2)

 They both contain the same amount of foreign substance. back to puzzle

(3)

 Burn rope 1 at both ends, at the same time burn rope 2 at one end. As soon as rope 1 burns out (30 minutes), burn rope 2 at the other end. When rope 2 burns out, the time is 45 minutes. back to puzzle

(4)
 i) Ball numbered as 1~9. ``` weigh 123 and 456, if balanced then weigh 7 and 8, if balanced then 9 is bad. else weigh 7 and 9, if balanced then 8 is bad. else 7 is bad. else (suppose 123 is heavier), weigh 14 and 25, if balanced then weigh 3 and 7, if balanced then 6 is bad. else 3 is bad. else (suppose 14 is heavier), weigh 1 and 7, if balanced then 5 is bad. else 1 is bad. ``` ii) Ball numbered as A, B, C, D, ... ``` weigh ABCD and EFGH, if balanced then weigh IJK and ABC, if balanced then L is bad else (suppose IJK is heavier), weigh I and J, if balanced then K is bad. else the heavier one is bad. else (suppose ABCD is heavier), weigh ABE and CDF, if balanced then weigh A and G, if balanced then H is bad. else G is bad. else if ABE is heavier, we know that the bad one is A, B or F; if ABE is lighter, we know that the bad one is E, C or D. suppose ABE is heavier, weigh AF and IJ, if balanced then B is bad. else if AF is heavier, then A is bad. else F is bad. ``` Following the instruction above, one can also tell whether the bad one is heavier or lighter without any extra weighing. back to puzzle

(5)

 Fasten one end of the rope on the tree on the bank. Carry the other end and go along the bank of the lake. As it is a lake, eventually, you will come back to the tree and at that time the rope is already circled around the tree on the island. back to puzzle

(6)

 Tom will always win if Jerry goes first. Every time Jerry goes, Tom shall take an appropriate step that leaves PAIRS (either 1 or 2) of piles with the same number of chess pieces in each pile of a pair (say 3344, 0044, 0011, ...). Finally, the 00XX will become 0000. back to puzzle

(7)

 Orientation of the word "coin" will be the same as before (not upside-down). back to puzzle

(8)

 For rooms 2, 3, 5, and 6, A can win B. For rooms 1 and 4, A can never win. (You figure out how.) back to puzzle

(9)

 See the following picture. back to puzzle

(10)

 For square-shaped cake, we need N+M cuts. For round cake, N+M-1 cuts. If we have N, M, K, then the answers are N+M+K and N+M+K-2 respectively. (You figure out how.) back to puzzle

(11)

 The tangent of lower-left angle of the red triangle is 3/8 while that of the green triangle is 2/5. They are not equal, which means the "diagonal" of the big triangle is not a straight line. It bends down a bit in the first picture, and bends up a bit in the second. The difference of these two tiny bends makes you twist your brain until now. back to puzzle

(12)

 I found 12 naturally recognizable faces with their noses circled in red. back to puzzle

(13)

 I can only find 4 with their heads circled in red. back to puzzle I can find 5 for this one. (Thanks to Ana from Portugal for the original pciture.)

(14)

 I can't explain it. :( back to puzzle