Sunday Puzzles

[Robb27]

Sunday 27th September

DATA = 8797 and FACTS = 17594
-When summing 2 numbers like this, carry forwards, if there are any, can only have a value of 1. Therefore F=1
-The only possible solution for T + T = T is for there to be a carry forward from A + A = S. Hence T + T + 1 = T, which only has one solution when T = 9, as 9 + 9 + 1 = 19.
-Then as A + A = S gives a carry forward and 0 is not valid, A is either [6, 7, 8]
-Given that A + A = C also gives a carry, therefore D + D + 1 = A. The only possible integer solution is when A = 7 (otherwise A would be with 2.5 or 3.5!)
-Using this, S = 4 and C = 5
-Finally, to get F = 1, D + D + 1 = A has to give a carry. Rearranging 2D = A – 1 = 6 therefore D could only be either [3, 8] but as 3 would not give a carry, D must be 8.

This is the only solution given T=9 and that A must be odd but can’t be 5 as zero is not allowed.

Additional:
If zero WAS allowed, A could = 5 giving another solution: DATA = 7595 and FACTS = 15190

[darjeeling]

The problem says that the number zero is not allowed as the leading digit of DATA or FACTS, and so neither D nor F can be zero. It does not (directly) preclude zero from occuring elsewhere in the numbers. So your solution is missing some extra logic to explain why A=5 is not possible.

(Your additional solution with A=5 does not work because you are setting both F and C to 1…)

[Robb27]

@darjeeling
Thanks… my incorrect (ahem, need to double check before posting!) additional, actually shows why A can’t be 5 as it leads to both F and C being 1, as you rightly point out.

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