Velvet Ties (Posted on 2008-02-25)

	Submitted by K Sengupta
Rating: 3.5000 (2 votes)
Solution:	(Hide)
VELVET = 183184, TIE = 428 183184 = (428)*(428) EXPLANATION: Since the result of the multiplication is a six digit number, it follows that T ≥ 3. Also the last digit of the result, which is a perfect square, is represented by T, and accordingly, T = 4, 5, 6, 9. If T=5, then we must have E=5, which is a contradiction. A similar violation corresponding to the provisions of the problem occurs whenever T=6, which gives E=6. Thus, T = 4 or 9. If T=4, then the last digit of VELVET is 4 only when E = 2 or 8. Likewise, if T =9, then it follows that E = 3 or 7. This leads to the following cases. Case (i) : 4I2*4I2 = V2LV24, for I != 2, 4 Case (ii) : 4I8*4I8 = V8LV84, for I != 4, 8 Case (iii) : 9I7*9I7 = V7LV79, for I != 7, 9 Case (iv) : 9I3*913 = V3LV39, for I != 3, 9 Of all the four cases, only case (i) yields a valid solution, that is: 428*428 = 183184, whenever V=1, I=2, L=3, T=4 and E=8

	Subject	Author	Date
	velvet ties - solution	ed bottemiller	2008-02-26 12:33:41
	re(2): Solution	Dej Mar	2008-02-26 00:27:31
	re: Solution	Josie Faulkner	2008-02-25 12:59:56
	Solution	Dej Mar	2008-02-25 12:31:04