Four Fours is a puzzle old enough to appear in 19th-century books of recreational math. The rule is simple — write the digit 4 exactly four times, and freely place the four operations (+, −, ×, ÷) between them to build whatever number you like. The constraint of repeating just one number, 4, is exactly what makes this puzzle so appealing — it turns into a challenge of how many different values you can squeeze out of one seemingly ordinary digit.
The four operations alone can't reach very many numbers. So Four Fours usually allows a few extra moves — applying √ (square root, √4=2), attaching ! (factorial, 4!=24×1=24), and joining two 4s with no symbol between them into the two-digit number 44. Factorial alone can turn a 4 into 24, and joining suddenly turns two 4s into the much bigger number 44 — both dramatically widen what's within reach. Add in the ability to group a pair and calculate it first (parentheses), and just four 4s are enough to build every whole number from 0 to 32.
What's interesting is how much the difficulty varies from number to number. Some numbers come easily, like 4+4+4+4=16 or 4+4+4×4=24, while others take real effort to find. 7, for example, only comes out if you use the fact that division is calculated before addition and subtraction — 4+4−4÷4 — and an odd prime like 13 can be a real struggle with just the four operations, eventually requiring both factorial and square root together, as in 4÷4+4!÷√(4). 44 is as simple as joining two 4s, like 4+44−4, and even numbers 33 and above, like 35, become reachable thanks to joining — 44÷4+4!=35. That said, not every number 33 and above can be solved with these particular rules (fixed order, √·!, pairing two at a time, joining) — some numbers still remain out of reach, and solving those would require a broader rule that allows freely reordering the four 4s.
Working through this puzzle naturally builds a hands-on feel for order of operations (multiplication and division before addition and subtraction) and what parentheses are for. It also builds the instinct that "there's often more than one right answer" — because the same number can frequently be reached by more than one expression. Just asking yourself "is there another way?" after building the target number doubles the thinking practice you get.
On our activity page, you can press the √·! buttons above each of the four 4s to decorate them, then drag +, −, ×, ÷, and the "44" tile (for joining) from the symbol palette below into a slot. The "Group first pair" and "Group last pair" buttons let you control the parentheses yourself, too. If you get stuck, use the hint button to see one example answer.