77 and Four 4s

Chloe’s math teacher gave the kids a challenge. Using the number 4 exactly four times in an equation, arrive at the numbers 1-100 in the answers.

Using the number 44 as part of the equation counts as two 4s. You can use 4 to the zero power to represent the number 1. 4! equals 24. The square root of 4 equals the number 2, etc.

The first three kids to turn in the 100 equations get a prize. Chloe, as is her wont, jumped to the challenge and obsessively started working on the puzzle as soon as she got home from school yesterday. Determined to finish in less than a day, even though her teacher told the class it’s taken previous students two weeks to complete.

And this morning, she had only one number left to solve: 77. When she got home from school, she called me to ask if I figured it out. Which I hadn’t. But I scribbled on my piece of paper a few more times, in between responding to emails, and I got it. I called her to give her a single hint: if she’s allowed to use a number to the 4th power, she should use it and a parenthetical.

Three minutes later, she had it solved. And for those if you wondering how to get to the number 77 using only four 4s, here you go:

[(4-4^0)^4] -4 = 77.

Chloe never gives up. She perseveres until she finishes what she’s started. Just like her mom.


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