## Teaser 2997: Cemetery lottery symmetry

**From The Sunday Times, 1st March 2020** [link]

Our local cemetery conservation lottery tickets have four numbers for a line. Using eight different numbers, my two lines have several symmetries. For each line: just one number is odd; there is one number from each of the ranges 1-9, 10-19, 20-29 and 30-39, in that order; the sum of the four numbers equals that sum for the other line; excluding 1 and the numbers themselves, the 1st and 2nd numbers share just one factor — as do the 2nd and 3rd (a different factor) and the 3rd and 4th (another different factor) and, finally, the 4th and 1st.

Printed one line directly above the other, my top line includes the largest of the eight numbers.

What is the bottom line?

[teaser2997]

## Jim Randell 5:31 pm

on28 February 2020 Permalink |This Python program runs in 239ms.

Run:[ @repl.it ]Solution:The numbers on the bottom line are: 6, 15, 20, 34.The numbers on the top line are: 4, 14, 21, 36.

These are the only two candidate lines that have the same sum (they both sum to 75).

There are three other candidate lines, but they all have different sums.

The full list of candidate lines is:

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## Frits 12:26 pm

on24 December 2020 Permalink |LikeLike