The alphametic: PSEUD + SUSAN = DENHAM does NOT have any solution in base 10.
Determine the minimum value of a positive integer b≤36, such that the said equation has at least one solution in base b.
If I refer to a column by number, it is counting from right to left.
Give the value of each carry a variable name:
zyxw
PSEUD
SUSAN
-------
DENHAM
D must be 1 from column 6.
E < b-1 from column 5. max of z is 1, max of the pair P&S is b-1 and b-2.
E = z + P + S - b
case1: N=b-1
then M=0, carry w=1, U=b-1 since w+U+A ends in A in the second column
both N and U cannot be b-1. Contradiction.
case2: N≠b-1 (in fact N < b-1)
then M=N+1, carry w=0, U=0, carry x=0 <-- must be True.
We have:
U=0, D=1, M=N+1, w=0, x=0, M>2, E < b-1, and E = z + P + S - b
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Posted by Larry
on 2024-07-04 12:09:56 |
Starting analysis