Brain Teasers
Little Johnny
Little Johnny was trying to work out a Math-Magic problem his teacher had given him at school that day. He was having problems, so he asked his mom to help.
The problem read, MAD + AS + A = BULL
"Mom", he said, "I need to use some of the numbers from 0-9 to make this problem work. I have already figured out from Skippy at school that D equals 3 and L equals 7, but I can't get the rest. Each letter stands for only one number."
His mother helped him figure out the rest. Can you figure out the answer, given what Little Johnny already knew?
The problem read, MAD + AS + A = BULL
"Mom", he said, "I need to use some of the numbers from 0-9 to make this problem work. I have already figured out from Skippy at school that D equals 3 and L equals 7, but I can't get the rest. Each letter stands for only one number."
His mother helped him figure out the rest. Can you figure out the answer, given what Little Johnny already knew?
Answer
983 + 86 + 8 = 1077 is the answer, based on what Johnny knew at the beginning.Hide Answer Show Answer
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Comments
This was pretty hard , but EZ in the end!!
Yay! First one!
Yay! First one!
Hi, how about adding the letters' values:
A=8 B=1 D=3 L=7 M=9 S=6
A=8 B=1 D=3 L=7 M=9 S=6
Right!??
that was hard, i could not get it, i am not very good at math-magic problems
Got lazy and just checked, figuring I was close. More simple than originally expected as, D + S + A = XL (where X is an irrelevant digit), that is to say D+S+A = something that ends in L. Knowing they are all unique digits, and that D=3 and L = 7, we get 3 +S+A = 7, leaving us with S=2,A=2 (rejected) or one of them =1, the other 3 (also rejected - no number represented by two different letters) and since D+S+A will not equal 27 as all unique digits (3 9's would work, obviously, but, D=3, no repeats, etc, etc), they must add to 17, leaving S and A to equal either 9 and 5 or 8 and 6 (can't repeat the 7), though the order isn't known. Now, a 3 digit plus a 2 digit plus a 1 digit = a four digit number. The absolute lowest the 3 digit number could EVER be, would be 892, witht he 2 digit being 99 and the one digit being 9. We know that D = 3, so try 893 +95(rule from before) + 9 < 1000, therefore the answer must lie somewhere with M = 9. Given that premise, the only possibilities are 983 +86 +8 or 963 +68 +6, with only the first one equalling 1077, that is, the last two digits both 77, another premise necessary to meet. I am assuming that was the only way to do the problem, but if there was a quicker way, I'd be interested to hear it.
It was very easy; I did it in my head in about 20 seconds.
In the 10s place there is A + A = 7, so there has to be a carry of 1 from the 1s column and A is either 3 or 8, but it can't be 3 since D is 3, so A = 8. If A is 8 then S = 6 in the 1s. Since BULL has four digits and M is the only number in the 100s, M must be 9, which makes BU = 10.
I think that's a bit simpler than Jake's solution.
In the 10s place there is A + A = 7, so there has to be a carry of 1 from the 1s column and A is either 3 or 8, but it can't be 3 since D is 3, so A = 8. If A is 8 then S = 6 in the 1s. Since BULL has four digits and M is the only number in the 100s, M must be 9, which makes BU = 10.
I think that's a bit simpler than Jake's solution.
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