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17 April, 19:07

Write one digit on each side of 73 to make a four digit multiple of 36. How many different solutions does this problem have?

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  1. 17 April, 19:26
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    Answer: an option is 2736

    and we only have two possible solutions, the other is 6732

    Step-by-step explanation:

    we want to write a number:

    a73b, where a and b are one digit numbers (0 to 9) in such way that the number is divisible by 36.

    Now, we know that 36 is multiple of 6, so 6*6 = 36

    The multiples of 36 are always even numbers, so we can discard all the odd options for b.

    We also can discard the option a = 0, because we want a 4 digit number.

    now, let's do it by brute force.

    if a = 1, we have:

    173b, now you can give b different values (only even values) and see if some of them is divisible by 36. You will find that none is.

    if a = 2

    273b

    when b = 6, we have:

    N = 2736, that is divisible by 36 as:

    2736/36 = 79, so this is a multiple of 36.

    now, you can keep changing the value of a and find all the different possible solutions.

    if a = 3,

    373b is not divisible by 36 for any value of b

    if a = 4

    473b is not divisible by 36 for any value of b

    if a = 5

    573b is not divisible by 36 for any value of b

    if a = 6

    673b it is divisible by 36 when b = 2.

    6732/36 = 187

    if a = 7

    773b is not divisible by 36 for any value of b

    if a = 8

    873b is not divisible by 36 for any value of b

    if a = 9

    973b is not divisible by 36 for any value of b

    So we only have two possible solutions
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