The Trader's Puzzle - Balance Weights

What are the weights of the four rings to as to measure any desired weight from a quarter-pound up to ten, in quarter-pound increments?

Lake Puzzle

see the answer here.

Archery Puzzle

How close can the young archer come to scoring a total of 100 - using as many arrows as she pleases.
The rings are numbered 16, 17, 23, 24, 39, 40

Skating Puzzle

It is recorded that in a mile race between two graceful skaters the rivals started from opposite points to skate to the other's place of beginning. With the advantage of a strong wind Jennie performed the feat two and a half times as quick as Maude, and beat her by six minutes. The problem, which has created no end of discussion, is to tell the time of each in skating the mile.

Cattle Puzzle

Farmer Jones sold a pair of cows for $210. On one he made 10 percent and on the other he lost 10 per cent, cleaning up just 5 per cent. What did the cows originally cost him?

Sam Loyd, Cyclopedia of Puzzles, 1914

answer here.

The Milkman's Puzzle

Honest John says that what he "don't know about milk is scarcely worth mentioning," but he was flabbergasted the other day when he had nothing but two ten-gallon cans of milk, and two customers with a five and a four quart measure wanted two quarts put into each measure.

It is a juggling trick, pure and simple, devoid of trick or device, but it calls for much cleverness to get two exact quarts of milk into those measures employing no other receptacles of any kind except the two measures and the two full cans. You can try the problem with the fullest assurance that it is a legitimate and not a silly catch.

Sam Loyd, Cyclopedia of Puzzles, 1914

see the answer.

The Weight of a Brick

If a brick balances with three-quarters of a brick and three-quarters of a pound, how much does a brick weigh?
~Sam Loyd, Cyclopedia of Puzzles, 1914

I won't bother with a separate post: answer

How Old is Mary?

"You see," remarked GrandPa, "the combined ages of Mary and Ann are 44 years, and Mary is twice as old as Ann was when Mary was half as old as Ann will be when when Ann is three times as old as Mary was when Mary was three times as old as Ann.
How old is Mary?

~ Sam Loyd, Cyclopedia of Puzzles, 1914

Clock Puzzle

The picture of a clock dial illustrated the important point of evidence in a detective story where a stray bullet from the assassin's pistol struck the face of the clock.

It struck the exact center, driving the post through the works and stopping the clock. The two hands became united, as it were, in one line, pointing in opposite directions, although not in the direction shown, for it is evident that the hands could not point at three and nine at the same time.

Can you tell what time of day it must have been, thereby proving an alibi for the hero who wishes to show he was eating a plate of pig's knuckles in Hoboken at the time the pistol was fired in Sir Reginald's flat in Harlem?

- Sam Loyd, Cyclopedia of Puzzles, 1914


answer in this backdated post.

Cats and Kittens Puzzle

Seeing that four cats and three kittens weigh thirty-seven pounds, while three cats and four kittens weigh but thirty three pounds, we are asked to tell the respective weights of cats and kittens.

- Sam Loyd, Cyclopedia of Puzzles, 1914

The Missing Word Puzzle

"Here is an odd little criss-cross puzzle wherein you are to discover a word, which when placed in the vacant space, so as to be read twice, will make the sentence complete, beginning at THE and ending with ESCAPED.
- Sam Loyd, Cyclopedia of Puzzles, 1914

The Lily-Pad Problem

Proposition – If the water lily is ten inches above the water, and disappears under the surface at a point distant twenty-one inches, what is the depth of the lake?

Click title to Read further

The Milkman's Puzzle - answer

I haven't really thought this out fully, so there may be a better answer (I might have done a logical circle) or one in fewer steps.

The assumption is that we will, every time, pour milk until the RECEIVING vessel is full or until the pouring vessel is empty. There are no half-pours or "holding the pitcher at an angle so as to get half a can." Label the containers 4, 5, A and B.

4 5   A  B 
A -> 4    4 0   6 10
4 -> 5    0 4   6 10
A -> 4    4 5   2  9
4 -> B    3 5   2 10

5 -> A    3 0   7 10
4 -> 5    0 3   7 10
B -> 4    4 3   7  6
4 -> 5    2 5   7  6 
5 -> A    2 2  10  6

Back to the puzzle.

Lake Puzzle Answer

I used Heron's Law the first time I solved this and a buncha triangles the second time I tried. I kept getting 11 acres but, as jd mentioned in the other comment, the elegant solution must be available but it escaped me every time I tried.

The puzzle solution relies on the recognition of three pythagorean triangles. (How one came to these combinations was never quite clear to me, but hey ...)

5-7-√74 triangle would have the same length side as a square of area 74 sq. units.
4-10-√116 would have the same length side as the square of area 116
9-17-√370 triangle would have the same side as a square of area 370

Lo and behold, these triangles could be rearranged as below.

The lake is therefore the difference in area of the big triangle (0.5*9*17 = 76.5) and the three smaller pieces (28 + 0.5*5*7 + 20 = 65.5) which is 11.

So there you have it. In my opinion, this proves that the solution works but gives no indication (to me at least) of how one might solve similar situations in the future and does not enlighten the puzzler to some heretofore unknown rule, theorem or hypothesis. Not a very satisfying solution for me.

return to the puzzle.