Can 5 7 7 7 make 24? No.
An exhaustive search over every arrangement of these four numbers with + − × ÷ — fraction intermediates included — never reaches 24. 458 of the 1820 four-number combinations are unsolvable. The closest hands that do work:
Solving hints
Build a factor pair: split the four numbers into two groups and try to make a factor pair of 24 — 3 × 8, 4 × 6, or 12 × 2 — then multiply the two groups.
No factor pair divides cleanly? Switch to sums: make two numbers add up to 24, or try shapes like (a ± b) × (c ± d) and (a + b + c) × d.
These nearby hands can make 24:
FAQ
Can 5 7 7 7 make 24 if fractions are allowed?
No. Even with fraction intermediate steps allowed, an exhaustive search over every combination of + − × ÷ finds no way to reach 24 from 5 7 7 7.
Which hands near 5 7 7 7 are solvable?
Change any one of the four numbers and a solvable hand is usually nearby — the related hands listed above all make 24.