BÀI TOÁN. Dùng các số từ $1$ đến $9$ (mỗi số xuất hiện đúng $1$ lần) và các phép toán cộng $(+)$, trừ $(-)$, nhân $(\times)$ để viết thành một biểu thức có giá trị bằng $100$?
Một biểu thức thỏa mãn yêu cầu trên là:
Điều thú vị là nó còn có hàng loạt lời giải khác.
$1+2+3+4+5+6+7+8\times9 = 100$
$198-73-26+5-4=100$
$56+49-2-3+8-7-1=100$
$6\times7\times2+8-3+1+9-4+5=100$
$(5\times6)+(4\times9)+(8\times3)+7+2+1 = 100$
$123-4-5-6-7+8-9 = 100$
$69+31+8+5-7-4-2 = 100$
$231-(9\times8)-(6\times5)-7-4=100$
$(1+9+2+8) \times 5 + (3+7) - (4+6)=100$
$9\times4\times2 + 8 + 7 + 3 + 5 + 6 - 1 = 100$
$9\times8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 = 100$
$9\times8 + 4 * 7 - 5 * 2 + 6 + 3 + 1 = 100$
$98+7-6+5-4+3-2-1=100$
$2 \times (7 \times 8 \times 9 - 456) + 3 + 1=100$
$(9 \times 8) + (7 \times 6) - (5 \times 4) + (3 \times 2 \times 1)=100$
$25\times4 - 9 + 6 + 3 - 7 + 8 - 1=100$
$92 + 6 + 3 - 4 + 5 - 1 + 7 - 8=100$
$(51+4+3) \times 2 -9-8 + 7 -6=100$
$89+7+6-5+(2\times3)-4+1=100$
$(7 + 3) \times 9 + 5 + 4 + 1 + 8 - 6 - 2=100$
$9\times8+1+2+3+4+5+6+7=100$
$6\times3\times5+12+4+(9-8)-7=100$
$9\times8+7+1+5\times6-(4\times3-2)=100$
$[(1+2+3+4) \times 9] + 5 + 6 + 7 - 8 = 100$
$123+45-67+8-9=100$
$98-7-6+5+4+3+2+1=100$
$(1+2+3+4+5)\times6-7+8+9=100$
$8\times9 +7 +1 +5 +6 +4 +3 +2 =100$
$12+34+59-6+8-7=100$
$68 + 23 + 15 -4 +7 - 9=100$
$(9\times8) + 1 + 2 + 3 + 4 + 5 + 6 + 7=100$
$(98-7) +1 -4 +6 -2 +3+5=100$
$4\times(5+7+8) + 1\times(2+3+6+9)=100$
$25 + (8\times9-4) + 13-(6+7)=100$
$963-852-7-4\times1=100$
$6\times9\times2-8+4+1-3+5-7=100$
$9\times6+34+7+8-5+2\times1=100$
$9\times7+(6\times8)-5-4-3-1+2=100$
$(9\times7) + 6 + 1 + (5 \times 2) + (4 \times 3) + 8=100$
$(9+1)-(2+8)+(3+7)+(4+6)\times5=100$
$8\times9+67+1-45+2+3 =100$
$5\times19+34-28-7+6=100$
$3\times4\times6+2\times9+(8-7+1)\times5=100$
$8\times9+1+2+3+4+5+6+7=100$
$156-78+29-3-4=100$
$5\times9=45, 45+7=52, 52\times2=104, 104-6=98, 98+4=102, 102-3=99, 99+1=100$
$78+24+9-6-5+3-2-1=100$
$1+8\times9+2+7+6+5+3-4=100.$
$9\times8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 = 100$
$(9\times8) + 7 + 6 + 5 + (4 \times 3) - (2 \times 1) = 100.$
$(6+4)\times(8+9-7+5-3-2)\times1 = 100.$
$1 + 2 + 3 + 4 + 5 +6 + 7 + (8\times9) = 100$
$(1+7+2) \times 9 + 8 + (4\times5)- (3\times6) = 100$
$9-1=8, 8-2=6,7-3=4, 6-4=2, 8+6+4+2=20\times5=100.$
$(124-3-5-6-8-9)+7 = 100$
$(5\times7\times2\times1)+3+4+6+8+9 = 100$
$(1+2\times3\times4)\times5-6*7+8+9=100.$
$9\times8+7+(6\times4)-5+1+3-2=100.$
$4\times5\times6-7-8-9-1+2+3=100$
$24\times5-9-8-7+6+1-3=100$
$9\times8+1+2+3+4+5+6+7=100$
$(9\times8)+7+6+5+4+3+2+1 = 100.$
$(9+8) \times 7 - 6 \times 5 + 4 \times 3 + 1 - 2=100$
$(1 + 9 + 2 + 8 + 3 + 7 - 6 - 4) \times 5=100$
$91+82-67-5-4+3=100$
$(6+4)\times9+7+3+1+2+5-8=100$
$7\times5\times4-9\times3-8-6+2-1=100$
$12\times5+39+6-8+7-4=100.$
$9\times(6+3)+1+8+7+2+(5-4)=100$
$2\times(6\times9-3-1+8-5-7+4)=100$
$7\times9+4\times3+5+6\times2+8\times1=100$
$1\times(932-845)+6+7=100$
$5\times6+87+1-9-4-3-2=100$
$9\times8+7+6+5+4\times3-2\times1=100$
$8 \times 9 + 7 + 1 + 6 + 5 + 4 + 2 + 3 = 100$
$(1 + 2 + 3 + 4 + 5) \times 6 + (8 + 9) - 7 = 100$
$341 - 265 + 9 + 7 + 8 = 100$
$91 + 7 + 2 + 5 + 8 - 3 - 4 - 6 = 100$
$123 - 45 - 67 + 89 = 100$
$8 \times 9 \times 2 - (4 \times 5) - (6 \times 3) - 7 + 1 = 100$
$(1 + 2 + 3) \times 6 - 7 - 5 - 8 + 9 \times 4 = 100.$