522641637527417426415375.

Yet reflect a moment and all will be clear. Divide the 24 figures into 2 groups of 12 figures each and number the first group, divided into four sections, thus:—

(1)(2)(3)(4)
522,641,637,527.

Now bring the first and fourth groups into relation, and you see at once that the fourth group is larger than the first group by only five. Bringing the second group into relation with the third group, we find they differ only by four. Again: the third group is larger than the fourth by 100 and by 10, that is 527 becomes 637, the seven alone remaining steadfast. Beginning with the fourth group and passing to the third group we have the fourth group with 110 added. The second group is the third group with only four added, and the first group is the fourth group with only five subtracted. Thinking out these relations you can recall the groups as groups or the separate figures of each group or the entire 12 figures either forwards or backwards—and you have achieved this result by Attention and Thought.

The other twelve figures are easily disposed of. They are 417426415375. Divided into groups of three figures each we have

(1)(2)(3)(4)
417426415375.

Bringing the first group into relation with the third group, we notice that it is larger by two—and considering the second group with the fourth group, we find that the second group is as much and one more above 400 as the fourth is below 400. Other minor matters could be noticed, as that the first two figures of each group are respectively 41—42—41—37, and that the last figure in each group is 7—6—5—5. But these relations are hardly worth observing.

Coming back to the first series, we know that each figure represents the number of the day of the month to which it belongs on which the first Saturday in that month falls.‌ The figures for 1895 are 522—641—637—527. The first Saturday in January, 1895, falls on the fifth day of January, hence the second Saturday must be 5 + 7 = the 12th day of January; the third Saturday the 19th, and the fourth Saturday 26th. It is easy to know on what day of the week any day in January falls. Suppose you ask on what week day the 25th of January falls? You know the 26th is Saturday, and hence the 25th must be the day preceding the 26th, to wit, Friday, the 25th. Suppose you ask on what week day the 9th of January falls. You know the 12th is Saturday (the second Saturday). You now count backward thus: 12 is Saturday, 11 must be Friday, 10 Thursday, 9 must be Wednesday. The first Saturday in January, 1895, is the 5th; of February, the 2nd; of March, the 2nd; of April, the 6th; of May, the 4th, &c., &c. And we can tell on what week day any day of any of the other months falls.

Exercises.

  1. —The Ratio of the Circumference of the circle to its diameter is expressed by the integer 3 and 708 decimals, of which I give only eight. Learning these nine figures is good practice in numeric thinking—3.14159265.
  2. —The Yellowstone National Park contains 2,294,740 acres.
  3. —The Monster Chartist Petition contained 3,317,702 names. [←ToC]