HYMNS

The Rev. Rundown of the Church of Diminishing Returns had a book of hymns numbered from 1 to 9999 called Hymns Ancient and Archaic. His reducing congregation was only prepared to sing one hymn each Sunday but even this was restricted because the Reverend had lost some of those white plastic tiles with numerals that slide into a wooden tablet to show which hymns are on the agenda. The only tiles the Reverend could find had the numbers 1, 4, 6, & 7 which rather restricted the number of hymns that could be chosen for the singular hymn each Sunday. However, he noticed that if the '6' tile were turned upside down, he could use it as the digit '9'. Hymn numbers could have from 1 to 4 digits. How many hymn numbers could be shown?

  ANSWER

These are the hymns numbers: 1 4 6 7 9 14 16 17 19 41 46 47 49 61 64 67 71 74 76 79 91 94 97 146 147 149 164 167 174 176 179 194 197 416 417 419 461 467 471 476 479 491 497 614 617 641 647 671 674 714 716 719 741 746 749 761 764 791 794 914 917 941 947 971 974 1467 1476 1479 1497 1647 1674 1746 1749 1764 1794 1947 1974 4167 4176 4179 4197 4617 4671 4716 4719 4761 4791 4917 4971 6147 6174 6417 6471 6714 6741 7146 7149 7164 7194 7416 7419 7461 7491 7614 7641 7914 7941 9147 9174 9417 9471 9714 9741

There are 113.

I received several answers, five in all, with the following persons getting it right: John Stafford, Susanne Bone, Richard Birkhill (who won the draw). Answers also from David Groom and Peter Wreford. Many thanks for your responses. Better luck next time to the losers.