School-Safe Puzzle Games

## Digging in the Dirt

Wow, this one is tricky-see if you can figure it out:

A boy comes upon a man digging a pit.

“Good morning,” he said. “How deep is that pit?”

“Try to Guess”, replied the man. “My height is exactly five feet ten inches.”

“How much deeper are you going?” said the boy.

“I’m going twice as deep,” was the answer, “and then my head will be twice as far below ground as it now above ground.”

Any thoughts? Feel free to submit your answer in the comment section below; will unmask before the week is over.

### 32 Comments to “Digging in the Dirt”

1. michaelc | Profile

I take when he says “my head”, he means the top of his head.

If we let the the distance above the ground be x, and the depth of the hole equal y, we can see that when he digs it twice as deep, the hole must then equal 2y. And we also see that the top of his head is below the ground by a distance of 2x. Also before he digs we see, 70 = x + y . (the depth of the hole plus the portion above ground is his height)

So the entire depth of the hole is 2y. The man’s height is 70 inches, and the distance from the top of his head to the top of the hole (the ground level) is 2x. So 2y = 70 + 2x.

So a little substitution, and you see that x = 17.5 and y=52.5.

So the hole is 52.5 inches, his head is sticking out 17.5 inches. When he digs twice the depth, the hole will be 105 inches, so 35 inches will be from ground level to the top of the man’s head.

I always found it easier to guess with some math help. Silly me.

2. Falwan | Profile

Is that you ,Dr. RK, digging for puzzles?

3. Falwan | Profile

pit is 3 feet 6 inches…

depth = x

head above by = 70 – x

head below by = 2(70 – x )

equation to solve :

70 + 2(70 – x ) = 3x

x = 42 inches = 3ft. 6 in.

4. poopsicle | Profile

70-x=a
2a+70=2x

x=current depth
a=current height above ground

x=52.5in
a=17.5in

5. bigbossSNK | Profile

Visualizing the man in the pit simplifies the problem.
The man’s head is above ground. His height is 5’10”. Standing in the pit, his height corresponds to the depth of the pit after adding the length his head is above ground.
In math lingo, let x be the depth of the pit, h be the length his head is above ground. Then:
x+h= 5′ 10”
He also says that twice the current depth of the pit corresponds to his height after adding twice the current length between the ground and the top of his head. Again:
2x= 5′ 10” +2h
Elementary, x=4′ 4,5”
(I’m accustomed to the metric system, so if my math or notations are incorrect, point it out)

6. mrman | Profile

52.5 inches is what I came up with.

7. NitzOO | Profile

Y= man’s height = 5ft. 10 in. = 70 in.
X= pit’s depth
The initial circumstance, when the boy comes and questions the man:
Y = X+Z => X = Y-Z (a)
The final circumstance, after the man has dug the pit twice as deep:
2X = Y+2Z => X = (Y+2Z)/2 (b)
From (a) and (b) => Y = 4Z
Z = 17.5 in. = 1ft. 5.5 in.
X = 3Z = 52.5 in. = 4 ft. 4.5 in.
So the pit’s depth is 4 feet and 4.5 inches.

P.S.: Maybe the final result is incorrect; I’m not good with imperial units.

8. Shawn | PUZZLE GRANDMASTER | Profile

The pit is 52.5″ deep.

The pit is 52.5 inches deep (4’4.5″, leaving his head 17.5 inches above ground. The final depth will be 105 inches (8’9″ with his head 35 inches below.

10. Danthok | Profile

52.5″ deep

11. DanK | Profile

The man is 5ft 10in or 70in tall and no matter how far down he digs the top of his head will always be 70in from the bottom of the hole. So his goal is to dig until the top of his head is 140in (twice his height) from the rim of the hole or until the hole is 210in (17 ft 6in) which is 3 times his height. If he needs to go twice as deep to reach that goal then he is currently at 105in (8ft 9in).

12. joe | Profile

We assume the man is already in the pit (as in the photo and we let the present depth of the pit be x, and the height that he sticks out of the pit be y. This means that his height is equal to x+y.
(1) … x+y = 70 inches
(we will convert back to feet in the end this is easier to work with)

He says he will go down twice the present depth ( 2x) and that his head will then be twice the distance below as it is above (so 2y )

In other words his height plus this 2y will equal the pit height, 2x
(2) … 70″ + 2y = 2x

Solving simultaneous equations (1) and (2) gives
x = 52.5 inches … this is the answer as the boy asks how deep is the pit when he meets him (in feet it is four feet and four and half inches)

13. Ari | Profile

A=distance from his head to ground level
B=how much the rest of his torso is under ground (eg. the depth of the pit)
D=total depth when he is finished digging
The dude is 5ft10in in height which equals 70in.
…so:
A+B=70 => A=70-B
D=2A+70 = 2(70-B)+70)=2B
=> 4B=210
B=52,5in.

So when asked, his pit was 4ft. 4½ in. deep and he is aiming for
a 8ft. 9in. deep hole for whatever reason.

14. Cyberjar88 | Profile

Assuming the man had not yet started digging, the pit would be 11’8″ deep upon completion.

15. Blusummers13 | Profile

The current depth of the hole is 52.5 inches or 4 feet 4.5 inches.
The final depth will be 8 feet 9 inches.

16. Alchemist | Profile

The hole is currently 52.5″ deep.

17. pravinkumar1942@gmail.com | Profile

i guess 5ft 10 inch
because he head is at ground level now….
guys can u help me 2 solve this???

18. fuzzy | Profile

My answer is not pretty, but here goes.
The man’s hole is 52.5 inches, or 4 feet 4.5 inches, deep right now.
He is 70 inches tall. Right now he is 17.5 inches above and 52.5 inches below the ground. When the hole is twice as deep, or 105 inches, his head will be 35 inches below the ground, which is twice 17.5.

19. Guurzak | Profile

x = current depth of pit
70-x = current height of head above ground
2x-70 = later depth of head below ground

2x-70 = 2(70-x)
2x-70 = 140-2x
4x = 210
x = 52.5

test: 70 – 52.5 = 17.5
105 – 70 = 35 = 2 * 17.5 ?

20. Jimmy Anders | PUZZLE MASTER | Profile

4 feet, 4 and 1/2 inches, and boy is my skin crawling just thinking about touching all that sand… Eww!

21. brianu | Profile

The hole is 4’4.5″ and will be 8’9″

22. doubletime | Profile

how far was his head above ground to begin with? was he in the pit when the boy walked up?

23. jmart574 | Profile

The hole is 52.5 inches deep.
The man is 70 inches tall and his head is A inches above ground
Hole one is 70-A, hole two is 70+2A
Finding a hole twice as deep will be the equation (70-A)2=70+2A
A=17.5, 70 inches tall minus 17.5 inches above the ground will give you 52.5

24. TonyTKL | Profile

Assuming he has only started digging, his head will be 10 feet 20 inches below the sand.

25. RK | Founder | Profile

While I badly need a vacation Falwan, I’m unfortunately nowhere near a beach right now!

26. RK | Founder | Profile

most of our math champs seem to concur the answer is 52.5….

27. Annastique | Profile

I see all this math so this may be a stupid answer but he says i’m going twice as deep as my head is *above* around and is the hole is already as deep as him (to the top of his head) hes not going any deaper cuz his head is not above ground it is already below.

28. Annastique | Profile

I see all this math so this may be a stupid answer but he says i’m going twice as deep as my head is *above* ground and if the hole is already as deep as him (or in other words to the top of his head) hes not going any deeper cuz his head is not above ground it is already below.

29. barryt | Profile

I am 72 years old but I can still remember how to solve simultaneous equations
from 60 years ago!
If the hole is y” deep at the start and the man’s head is x” above the top,
x + y = 70″ (equation a).
When the hole is 3y” deep the man’s head is 2x” below the top, so
3y – 2x = 70 (equation b).
3y + 3x = 210 (equation 1 x 3
Solving simultaneous equations,
5x = 140, hence x = 28, y = 42
So the hole is 42″ deep at present and will be 126″ deep eventually.

30. RK | Founder | Profile

Very Nice Work, barryt! Welcome aboard

31. ben_stilwell | Profile

D is depth, A the length of man above ground

D = 70 – A
2D = 70 + 2A
2(70 – A) = 70 + 2A
140 = 70 + 4A
4A = 70
A = 17.5

So his head is 17.5 inches above ground, leaving the depth 52.5 inches.
Which works out. When the hole is twice the depth, 105 inches, the top of his head will be 35 inches below ground.

Depth: 52.5

32. hex | PUZZLE MASTER | Profile

I don’t know how i missed this one:
x+y=5’10”
2y-2x=5’10”
solve for y=52.5″ (hole depth)