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#### Find four numbers, the sum of which is 45, so that if 2 is added to the first number, 2 is subtracted from the second number, the third number is multiplied by 2 and the fourth number is divided by 2, then the four numbers so produced are all the same. What are the four numbers?

**Answer: ** 8 + 2 = 10
12 - 2 = 10
5 x 2 = 10
20 ÷ 2 = 1045

**Solution: **

#### Given two 2s, “plus” can be changed to “times” without changing the results: 2 + 2= 2 x 2. The solution with three numbers is easy too: 1 + 2 + 3= 1 x 2 x 3. What is the answer for 4 numbers and for 5 numbers?

**Answer: ** Solution for 4 numbers:
1 + 1 + 2 + 4= 1 x 1 x 2 x 4.
Solution for 5 numbers:
1 + 1 + 1 + 2 + 5= 1 x 1 x 1 x 2 x 4
1 + 1 + 1 + 3 + 3= 1 x 1 x 1 x 2 x 4
1 + 1 +2 + 2 + 2= 1 x 1 x 2 x 2 x 2

**Solution: **

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