# Alice and Her Daughters

One day recently, out of the blue, my sister Alice made this remark about her three daughters and herself:

“A few years from now, Daisy and I will be one and a half times as old as Beryl and Cheryl. The same number of years ago, when they were still all teenagers, Beryl and I were, in total, twice as old as Cheryl and Daisy. Also, Cheryl and I were one and a half times as old as Beryl and Daisy.”

What are their four ages now?

## Grand Prize Winner

Congratulations to James B. Northcutt of Fox Electronics for solving CrossNumber 56. There were no winners for Engineers' Sports Day.

## CrossNumber 58

In this CrossNumber, no number begins with zero and none is repeated.

The absence of DOWN clues is intentional.

## Across

null

1. Square, 6 Down ~ 4
5. Square
8. Square of (5 Across – 1 Across)
9. Square, 4 x 3 Down
10. Square of (29 Across – 1 Across)
11. Square of 4 Down
12. Square
15. Root of 13 Down
16. Square, 4 x 5 Across
17. Down – square root of 29 Across
18. Square of 17 Across
19. Square of (Root of 14 Down – Root of 12 Across)
22. Square of (Root of 11 Across – Root of 5 Across)
25. Square of (3 Down – 12 Across)
27. Square of 26 Down. Also root of 1 Across + root of 3 Down.
28. Prime, 1 Across + root of 10 Across
29. Square, 13 Down – 16 Across

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Cross Number 56

## Engineers' Sports Day

Answer: Gold 11, Silver 5, Bronze 3, Mechanical 102, others 82

Solution: There are only 11 combinations of numbers 1 – 13, excluding 8, adding up to 16: 1, 2, 13; 1, 3, 12; 1, 4, 11; 1, 5, 10; 1, 6, 9; 2, 3, 11; 2, 4, 10; 2, 5, 9; 3, 4, 9; 3, 6, 7; 4, 5, 7.

Forming a matrix for Mechanical (M), Civil (C) and Electrical (E) for Gold (G), Silver (S) and Bronze (B), only two sets of nine numbers can be formed such that all numbers are different.

A)

1  2  3
4  5  6
11  9  7

null

B)

1  2  4
6  3  5
9  11  7