name the various types of cryptarithms with examples
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1)Double true
Double true cryptarithms are alphametics where the letters spell the words describing numbers, so that the actual wording is also true. In the example above, the cryptarithm is true, twice.
First, reading off the words, ‘one plus two plus two plus three plus three is indeed equal to eleven’.
Second, we can solve the cryptarithm, making the following substitutions:
E = 1, H = 4, L = 7, N = 9, O = 3, R = 6, T = 8, V = 2, W = 0
The cryptarithm is solved: 391 + 803 + 803 + 84611 + 84611 = 171219
Double true cryptarithms are solved the same way as regular alphametics.
2)Roots, powers and division cryptarithms
Cryptarithms are not restricted to addition. We already saw some multiplication problems. Cryptarithms with other operations can also be fun. Here is a simple ‘power’ cryptarithm: (AA)B=ABA(AA)B=ABA Let’s take a look at how to solve this one. First, we are looking for a 2-digit number (identical digits), which, when raised to a certain power, gives a 3-digit number. The smallest 2-digit number that is possible is 11. The power cannot be larger than 2 because then we get a 4-digit result. It cannot be smaller than 2 because then we get either 1 (when B=0) or a 2-digit number (AA when B=1). That’s all we need! The solution is 112112 where A=1 and B=2.
That was pretty straightforward, but if you get stuck, try looking for additional information. One thing we can do is to look at the units digit of the answer. In the case above, notice that when the number is raised to a certain power, the units digit in the result stays the same as the original units digit.
Square root cryptarithms can also be challenging. Remember that these can be reversed and turned into a multiplication problem. ABC−−−−√=BCABC=BC is the same as BCxBC=ABC
Special words
Another fun genre is when the cryptarithms spell special words.
SATURN + URANUS = PLANETS.
There are three possible solutions for this cryptarithm.
hope this helps you.!!☺☺
here's your answer...!!☺
1)Double true
Double true cryptarithms are alphametics where the letters spell the words describing numbers, so that the actual wording is also true. In the example above, the cryptarithm is true, twice.
First, reading off the words, ‘one plus two plus two plus three plus three is indeed equal to eleven’.
Second, we can solve the cryptarithm, making the following substitutions:
E = 1, H = 4, L = 7, N = 9, O = 3, R = 6, T = 8, V = 2, W = 0
The cryptarithm is solved: 391 + 803 + 803 + 84611 + 84611 = 171219
Double true cryptarithms are solved the same way as regular alphametics.
2)Roots, powers and division cryptarithms
Cryptarithms are not restricted to addition. We already saw some multiplication problems. Cryptarithms with other operations can also be fun. Here is a simple ‘power’ cryptarithm: (AA)B=ABA(AA)B=ABA Let’s take a look at how to solve this one. First, we are looking for a 2-digit number (identical digits), which, when raised to a certain power, gives a 3-digit number. The smallest 2-digit number that is possible is 11. The power cannot be larger than 2 because then we get a 4-digit result. It cannot be smaller than 2 because then we get either 1 (when B=0) or a 2-digit number (AA when B=1). That’s all we need! The solution is 112112 where A=1 and B=2.
That was pretty straightforward, but if you get stuck, try looking for additional information. One thing we can do is to look at the units digit of the answer. In the case above, notice that when the number is raised to a certain power, the units digit in the result stays the same as the original units digit.
Square root cryptarithms can also be challenging. Remember that these can be reversed and turned into a multiplication problem. ABC−−−−√=BCABC=BC is the same as BCxBC=ABC
Special words
Another fun genre is when the cryptarithms spell special words.
SATURN + URANUS = PLANETS.
There are three possible solutions for this cryptarithm.
hope this helps you.!!☺☺
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