**From New Scientist #2322, 22nd December 2001**

Each year there are eight presents in the sack, their values whole numbers of pounds from 1 to 8, to be distributed to the children Amber, Ben, Christine, and Dick. The presents are drawn from the sack at random, one at a time. Each is given to the child who has already received the lowest total value; if more than one qualify, then to whichever of them whose name comes first in alphabetic order.

Last year, Amber received a final total value of £8, Ben £5, Christine £11, Dick £12.

**Q1:** What were the values of the first and the seventh presents drawn?

I recorded the values in pounds for the previous five years:

1995: A 6, B 13, C 10, D 7

1996: A 10, B 6, C 14, D 6

1997: A 14, B 10, C 5, D 7

1998: A 9, B 5, C 12, D 10

1999: A 13, B 6, C 5, D 12

Unfortunately I must have made some mistakes because for some of those years the values could not have been achieved.

**Q2:** Which years were correctly written down?

Thanks to Hugh Casement for providing a transcript for this puzzle.

[enigma1166]

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This Python 3 program takes 449ms to check all six outcomes given in the puzzle and find all possible sequences that could lead to those outcomes. You can also use it to solve other problems by specifying the required outcomes and values on the command line.

Solution:Q1:The first present drawn was £2. The seventh present drawn was £7.Q2:The values given for 1995 and 1998 are correct.For

Q1there are four sequences that end with A=£8, B=£5, C=£11, D=£12:(£2, £5, £1, £4, £3, £6, £7, £8)

(£2, £5, £4, £1, £3, £6, £7, £8)

(£2, £5, £3, £4, £6, £1, £7, £8)

(£2, £5, £4, £3, £6, £1, £7, £8)

For

Q2there are no possible solutions for the values given for 1996, 1997, and 1999.For the values given for 1995 – (£6, £13, £10, £7) – there are 36 possible sequences that end with those values.

For the values given for 1998 – (£9, £5, £12, £10) – there are 8 possible sequences that end with those values.

So we assume that the values for these two years have been correctly recorded.