A magician asks you to choose two integers between 1 and 50 and add them.
Then add the largest two of the three integers at hand.
Then add the largest two again.
Repeat this around ten times.
Disclose to the magician your final number n.
The magician then tells you the next number.
How?
(In reply to
I would need a calculator (spoiler) by Steve Herman)
DEFDBL A-Z
CLS
FOR a = 1 TO 50
FOR b = a TO 50
x = a: y = b
FOR i = 1 TO 13
z = x + y
x = y: y = z
IF i >= 9 THEN
pred = INT(x * 1.618034 + .5)
IF pred <> y THEN
PRINT i, a; b, x, pred, y
END IF
END IF
NEXT
NEXT
NEXT
finds that the last failure is in trying to predict the ninth iteration from the eighth. The truncated version (1.618) starts to fail again trying to predict the 13th from the 12th.
The failures for gen 8 to gen 9 using the more accurate multiplier:
term to be a b prev predicted actual
predicted term
9 1 40 1381 2235 2234
9 1 41 1415 2290 2289
9 1 42 1449 2345 2344
9 1 43 1483 2400 2399
9 1 44 1517 2455 2454
9 1 45 1551 2510 2509
9 1 46 1585 2565 2564
9 1 47 1619 2620 2619
9 1 48 1653 2675 2674
9 1 49 1687 2730 2729
9 1 50 1721 2785 2784
9 2 42 1470 2379 2378
9 2 43 1504 2434 2433
9 2 44 1538 2489 2488
9 2 45 1572 2544 2543
9 2 46 1606 2599 2598
9 2 47 1640 2654 2653
9 2 48 1674 2709 2708
9 2 49 1708 2764 2763
9 2 50 1742 2819 2818
9 3 43 1525 2468 2467
9 3 44 1559 2523 2522
9 3 45 1593 2578 2577
9 3 46 1627 2633 2632
9 3 47 1661 2688 2687
9 3 48 1695 2743 2742
9 3 49 1729 2798 2797
9 3 50 1763 2853 2852
9 4 45 1614 2612 2611
9 4 46 1648 2667 2666
9 4 47 1682 2722 2721
9 4 48 1716 2777 2776
9 4 49 1750 2832 2831
9 4 50 1784 2887 2886
9 5 47 1703 2756 2755
9 5 48 1737 2811 2810
9 5 49 1771 2866 2865
9 5 50 1805 2921 2920
9 6 48 1758 2845 2844
9 6 49 1792 2900 2899
9 6 50 1826 2955 2954
9 7 50 1847 2989 2988
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Posted by Charlie
on 2013-12-26 13:34:29 |
re: I would need a calculator (spoiler)
