Problem:
F O R T Y + T E N + T E N = S I X T Y
Solution:
(digit 0) 2N = 0 (mod 10)
(digit 1) 2E = 0 (mod 10) no carry from digit 0 possible
Therefore N=0 and E=5.
Then O=9 and I=1 requiring two carries. Further S=F+1.
Digit 2 no gives the equation
R + 2T + 1 = 20 + X
The smallest digit left is 2. So X>=2
Therefore R + 2T >= 21. As not both R and T can be 7
one of then must be larger that is 8.
We are left with some case checkings.
Case R=8:
Then T>=6.5 that is T=7 and X=3. There are no consecutive
numbers left for F and S.
Case T=8:
Then R>=5 and as 5 is in use R>=6.
Case R=6: As X=3 there are no consecutive numbers left.
Case R=7: As X=4 we get F=2 and S=3. The remaining digit 6 will be Y.
Therefore we get a unique solution.
29786
850
850
-----
31486
References:
- Longley-Cook,
New Math Puzzle Book,
1970, p54
- Martin Gardner,
The Magic Numbers of Dr. Matrix,
1985
- Chapter 1: New York
Note: ELEVEN + TWO is an anagram of TWELVE + ONE.