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The puzzle that we will be solving today looks something like this,

S U J * Q M N

---------------

M A T M

J Q J J +

U T S U + +

---------------

U M S T A M

Follow the steps to solve the above puzzle:

S U 2 * Q 6 N

---------------

6 A T 6

2 Q 2 2 +

U T S U + +

---------------

U 6 S T A 6

Now assume N= 8 and T=3(as explained above) and rewriting we get,

S U 2 * Q 6 8

---------------

6 A 3 6

2 Q 2 2 +

U 3 S U + +

---------------

U 6 S 3 A 6

S U 4 * Q 6 N

---------------

6 A T 6

4 Q 4 4 +

U T S U + +

---------------

U 6 S T A 6

S U 4 * Q 6 9

---------------

6 5 1 6

4 Q 4 4 +

U 1 S U + +

---------------

U 6 S 1 5 6

S 2 4 * Q 6 9

---------------

6 5 1 6

4 Q 4 4 +

2 1 S 2 + +

---------------

2 6 S 1 5 6

7 2 4 * 3 6 9

---------------

6 5 1 6

4 3 4 4 +

2 1 7 2 + +

---------------

2 6 7 1 5 6

is the required solution.

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Also Check out:

**Elitmus pH Test Pattern & Syllabus****Tips For Elitmus Test****Tips To Solve Cryptarithmetic Puzzles**The puzzle that we will be solving today looks something like this,

S U J * Q M N

---------------

M A T M

J Q J J +

U T S U + +

---------------

U M S T A M

Follow the steps to solve the above puzzle:

**Step 1:**Look at the individual product term (S U J) * M = J Q J J. If you would have gone through the previous posts, you would guess the value of M=6 and J=2 or 4 or 8. Considering J as 2 and rewriting the puzzle we get,S U 2 * Q 6 N

---------------

6 A T 6

2 Q 2 2 +

U T S U + +

---------------

U 6 S T A 6

**Step 2:**Now (S U 2) * N = 6 A T 6, hence, N=3, 8. Let us assume N=3. Looking at the sum term 2+T=6, it is safe to assume that T=3 since a carry is most probably generated. But T cannot be 3, since N is already 3. So the assumption of N=3 is wrong.Now assume N= 8 and T=3(as explained above) and rewriting we get,

S U 2 * Q 6 8

---------------

6 A 3 6

2 Q 2 2 +

U 3 S U + +

---------------

U 6 S 3 A 6

**Step 3:**It is easy to note that A = 3+2 =5, also A+2+U = 3 i.e. 5+2+U=3, hence U=6. However, M is already 6. Hence the assumption of J=2 is not correct. Now assume J=4 as rewriting the equation we get,S U 4 * Q 6 N

---------------

6 A T 6

4 Q 4 4 +

U T S U + +

---------------

U 6 S T A 6

**Step 4:**(S U 4)*N = 6 A T 6, gives N=9. And the sum term 4+T+carry=6. Hence T=1. And T+4=A, i.e. A=5. Rewriting, we getS U 4 * Q 6 9

---------------

6 5 1 6

4 Q 4 4 +

U 1 S U + +

---------------

U 6 S 1 5 6

**Step 5:**The sum term, 5+4+U=1, which gives U=2. Therefore,S 2 4 * Q 6 9

---------------

6 5 1 6

4 Q 4 4 +

2 1 S 2 + +

---------------

2 6 S 1 5 6

**Step 6:**Now, (S 2 4)*9 = 6 5 1 6, gives S=7. And 6+Q+S=S i.e. 6+Q+7=7, gives Q=3. Therefore,7 2 4 * 3 6 9

---------------

6 5 1 6

4 3 4 4 +

2 1 7 2 + +

---------------

2 6 7 1 5 6

is the required solution.

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**Multiplication Cryptarithmetic Puzzle - 4****Solved Questions asked in eLitmus**
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