[bonanova]

Five points lie on a line.

When the 10 distances between each pair of them are

computed and listed from smallest to largest, we obtain

2, 4, 5, 7, 8, k, 13, 15, 17, 19.

What is the value of k?

[Guest]

12. Assume the five points are on the number line at indices 0,2,7,15,and 19. This produces differences of 2,7,15,19,5,13,17,8,12,and 4. Thus k = 12.

[Guest]

12

[Guest]

If we give names to points as a,b,c,d,e, the given series of 2,4,5,7... will reflect the values of e-a, e-b, e-c, e-b, e-a, d-c, d-b,......, b-a. Of course this order is not respectively.

But the sum of first series (90+k) must be equal to (e-d) + (e-c) + ... + (b-a).

If we open the paranthesis we see that 4e+2d-2b-4a = 90+k

or 2e+d-b-2a=45-k/2 ---> so k is en even number.

The largest gap is between e and a ---> so e-a=19

2(e-a)+d-b=45+k/2

2.19+d-b=45+k/2

d-b=7+k/2

From the given series, 8<k<13 ---> k=10 or k=12

if k=10 then d-b=7+5=12 but in the given series there is no 12.

if k=12 then d-b=7+6=13, there is 13 in the given series, so the answer is 12.