[Guest]

Solve this alphametic, where each of the capital letters in bold represents a different base ten digit from 0 to 9. None of the numbers can contain any leading zero.

73*(MUST) = STAND

Edited July 10, 2009 by K Sengupta

[Guest]

73* (1078) = 78694

Here's how:

T cant be 0 or 5 as it would make D the same

The max value of MUST is 1369; beyond that, 73*MUST becomes 6 digits

So, M = 1

The lowest value of MUST = 1023 and STAND is 7something

So S = 7 or 8 or 9

U can be 0, 2 or 3 only

If U = 3, S should be 9 but then MUST becomes > 1369 so U cant be 3

U can be either 0 or 2 only

If S = 8, then MUST can be max 1289 which gives STAND as 9 something, so S cant be 8

S must be either 7 or 9

Then, if S = 9, U must be 2 then STAND is always betweem 93 something and 94s omething

So T can only be be 4 but at MUST = 1294, STAND is 94462 NOT a possible solution

So, U should be 0 and S should be 7

we have 73*(107T) = 7TAND

Since 1072*73 = 78 something, the only possible value of T is 8

So, MUST must be 1078, and it matches the criteria!

Edited July 10, 2009 by DeeGee

[Guest]

Agree with DeeGee but got to it differently

There are only 3 cases where 73 is the multiplier, the product is 5 digits, the multiplicand is 4 digits and S & T are in the right place: (Excel

73*(1078) = 78694

73*(1186) = 86578

73*(1294) = 94462

Only 73*(1078) = 78694 does not have duplicated numbers in the product or multiplicand