The 4 4s problem… v100

Once again, credits to Enigmatic Code for providing the post.

Puzzle 55: Ton up

How can you divide 100 into four parts such that: adding 4 to the first part, subtracting 4 from the second part, multiplying the third part by 4 and dividing the fourth part by 4 results in all parts having the same value as each other?


This was extremely simple to solve, and I solved it in about 30 seconds.

Define the same value at the end of the puzzle to be “a”. Then, the four values can be represented as:

  • Adding: a – 4 (since adding 4 to a – 4 gives a)
  • Subtracting: a + 4
  • Multiplying: a/4
  • Dividing: 4a

These four parts all add up to 100, so a – 4 + a + 4 + a/4 + 4a = 6a + a/4, or 25a/4 = 100. Multiply each side by 4, and 25a = 400. Therefore, a = 16. The answer to the problem, however, isn’t the end result; it’s the beginning values. That’s simple:

  • a – 4 = 12
  • a + 4 = 20
  • a/4 = 4
  • 4a = 64

To double-check, 12+20+4+64 = 100. It works!

It’s amazing how things could seem extremely difficult on the outside, yet the solution is such a simple one.

Anyways, see ya in the next post!

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