Fun Mathy Type Riddles

[Whateverist]

Okay, I've gone to the shelf to find a few more:

1• A ball is dropped from a height of 40 feet.  It always bounces half the height it is dropped.  How far will it have traveled from the time it is dropped until the time it hits the ground the fourth time?



2• These toothpicks have been arranged to form four (small) squares.  Remove just two toothpicks so that only two squares are formed.  (Sorry about the lousy graphics.)
  _   _
| _ | _ |
| _ | _ |



3• You have only two buckets, one holds exactly 4 gallons of water and the other exactly 7 gallons.  Neither bucket contains any markings on it.  Using just these two buckets how can you bring back exactly 5 gallons of water?



4• A tray with 40 (identical) bolts weighs 500 grams.  The same tray holding 20 of the same bolts weighs 420 grams.  What is the weight of the tray?

Just for the bucket one since I love those ones.

---

  Fill the 4 gal, dump it into the 7 gal - leaving 3 gal empty space.
Fill the 4 gal again, dump it into the 7 gal until it is full - taking up the 3 gal of empty space and leaving 1 gal in the smaller bucket.
Empty the 7 gal on the floor.
Put the 1 gal from the smaller bucket into the big bucket.
Fill the 4 gal again, dump it into the big bucket to combine it with the 1 gal to make 5 gal.

---

And the ball one:

---

Ball drops 40ft *touch ground 1* -> total traveled = 40 ft
Ball goes up 20ft, then down 20ft *touch ground 2* -> total traveled = 40 + 20 +20 = 80
Ball goes up 10ft, then down 10 ft *touch ground 3* -> total traveled = 80 +10 +10 = 100
Ball goes up 5ft, then down 5ft *touch ground 4* -> total travel = 100 + 5 + 5 = 110 ft

That one was simple enough that I'm almost certain I missed something in the question.

---

---

Yep, I think the ball problem only catches anyone if they forget to count the upward bounce between each drop.

---