July 2, 2026 · Math
Four Fours Solutions: How to Make Every Number 1–100
The Four Fours puzzle asks you to write an expression for a target number using exactly four 4s and math operators. This guide gives you the toolkit that unlocks every number, clean worked solutions for 1–10, and tips for the hardest targets — then you can solve the rest in our free interactive game.
The one rule that matters
Use the digit 4 exactly four times — no more, no less. Everything else is fair game. The trick most beginners miss: joining digits counts. Writing 44 uses two 4s and 444 uses three — which is how you reach big numbers without running out of fours.
The operator toolkit
Each operator opens up a new set of reachable numbers. When you're stuck, run down this list:
44, 444Combine digits to make bigger starting numbers..4, .44Divide by a decimal to jump upward (÷ .4 ≈ × 2.5).4! = 24The fastest way to reach the 20s–90s.√4 = 2Turns a 4 into a 2 without spending an extra digit.4^4 = 256For overshooting, then dividing back down.44 % 8 = 4Remainders help land on exact odd targets.Worked solutions: 1 through 10
The first ten are the best warm-up — each one teaches a pattern you'll reuse higher up.
44 ÷ 444 ÷ 4 + 4 ÷ 4(4 + 4 + 4) ÷ 44 + 4 × (4 − 4)(4 × 4 + 4) ÷ 44 + (4 + 4) ÷ 444 ÷ 4 − 44 + 4 + 4 − 44 + 4 + 4 ÷ 4(44 − 4) ÷ 4Cracking the harder numbers
Above 20, the plain four-operations approach runs out of room. This is where the toolkit earns its keep — factorials, decimals, and roots do the heavy lifting:
4 × 4 + 4 + 4Straightforward once you spot 4 × 4 = 16.(4 + 4) × (4 + 4)Two groups of 8 multiplied together.44 ÷ .44Decimals unlock big jumps — .44 uses two 4s.4 × 4! + 4 − 4Factorial (4! = 24) reaches high numbers fast.4! + 4 + √4 + √4Mix factorial and square roots for the odd ones.Solve the rest yourself
We won't spoil all 100 — the fun is finding them. Our free game checks your expression live as you type, counts your fours, and shows the value climbing toward the target. No login, works on any device.
Play the Four Fours Challenge →Keep exploring
Frequently Asked Questions
What is the Four Fours puzzle?
Four Fours is a classic math puzzle: using exactly four 4s and standard math operations, write an expression equal to a target number. The goal is to hit every whole number from 1 to 100. It has been a recreational-math staple since the late 1800s.
How do you make 10 with four fours?
One clean answer is (44 − 4) ÷ 4 = 10. It uses the digit 4 exactly four times: the 44 counts as two, plus two more single 4s.
How do you make 100 with four fours?
A neat solution uses decimals: 44 ÷ .44 = 100. The 44 is two 4s and the .44 is two more, for four total.
What operations are allowed?
Standard versions allow +, −, ×, ÷, parentheses, exponents (^), square roots (√), factorials (!), decimals (like .4), and concatenation (44, 444). The exact rules vary; GeoProwl's game supports all of these plus modulo (%).
Do you have to use exactly four 4s?
Yes — that is the whole challenge. Not three, not five. Concatenating digits (44 uses two 4s, 444 uses three) is a key tactic for reaching bigger numbers.