BY THE NUMBERS

Fill in the entries of this crossword puzzle with a decimal point "." or a digit 0 through 9. All decimal values that are longer than the given number of blanks are truncated, not rounded.

ACROSS

1 ${15}^6+{189}^2$${15}^6+{189}^2$15^(6)+189^(2)15^{6}+189^{2}${15}^6+{189}^2$
6 Sum and product of its digits are equal
10 Number of primes less than 10,000
14 Acceleration of gravity in $\mathrm{m}/{\mathrm{s}}^2$$\mathrm{m}/{\mathrm{s}}^2$m//s^(2)\mathrm{m} / \mathrm{s}^{2}$\mathrm{m}/{\mathrm{s}}^2$
15 $\ln (2)/{\pi }^2$$\ln (2)/{\pi }^2$ln(2)//pi^(2)\ln (2) / \pi^{2}$\ln (2)/{\pi }^2$
16 Speed of light ____ $\times {10}^8\mathrm{m}/\mathrm{s}$$\times {10}^8\mathrm{m}/\mathrm{s}$xx10^(8)m//s\times 10^{8} \mathrm{~m} / \mathrm{s}$\times {10}^8\mathrm{m}/\mathrm{s}$
17 $(12+\sqrt{130})\pi$$(12+\sqrt{130})\pi$(12+sqrt130)pi(12+\sqrt{130}) \pi$(12+\sqrt{130})\pi$
18 Number of rook moves on a $16\times 16$$16\times 16$16 xx1616 \times 16$16\times 16$ board
19 Hardy's cab number
20 $0,1,4,\dots$$0,1,4,\dots$0,1,4,dots0,1,4, \ldots$0,1,4,\dots$
23 Water freezing temperature in Kelvin
24 A palindromic permutable prime
25 $2+\frac{1}{1+\frac{1}{56+\frac{1}{7}}}$$2+\frac{1}{1+\frac{1}{56+\frac{1}{7}}}$2+(1)/(1+(1)/(56+(1)/(7)))2+\frac{1}{1+\frac{1}{56+\frac{1}{7}}}$2+\frac{1}{1+\frac{1}{56+\frac{1}{7}}}$
28 Sum of the first four 4 th powers
29 Young Gauss's sum
31 Diagonal of a square with the same area as the unit circle
32 Look-and-say sequence
36 $1000(30+{\pi }^2)$$1000\left(30+{\pi }^2\right)$1000(30+pi^(2))1000\left(30+\pi^{2}\right)$1000(30+{\pi }^2)$
38 $10$$10$1010$10$ times the Basel problem sum
39 $2,3,5,$$2,3,5,$2,3,5,2,3,5,$2,3,5,$ ___
41 Smallest number whose square has eight digits
42 Location of the absolute minimum of $g(x)=x^6-420x+100$$g(x)=x^6-420x+100$g(x)=x^(6)-420 x+100g(x)=x^{6}-420 x+100$g(x)=x^6-420x+100$
44 $\tau$$\tau$tau\tau$\tau$
46 Emergency number in the US
47 $100e^e$$100e^e$100e^(e)100 e^{e}$100e^e$
49 Bronze ratio: $1+\sqrt{3+\sqrt{3+\sqrt{3+\dots }}}$$1+\sqrt{3+\sqrt{3+\sqrt{3+\dots }}}$1+sqrt(3+sqrt(3+sqrt(3+dots)))1+\sqrt{3+\sqrt{3+\sqrt{3+\ldots}}}$1+\sqrt{3+\sqrt{3+\sqrt{3+\dots }}}$
50 In Egyptian hieroglyphics:

$\cap \cap \cap \cap \cap \cap \cap \cap \cap \parallel$$\cap \cap \cap \cap \cap \cap \cap \cap \cap \parallel$nn nn nn nn nn nn nn nn nn||\cap \cap \cap \cap \cap \cap \cap \cap \cap \|$\cap \cap \cap \cap \cap \cap \cap \cap \cap \parallel$
52 Every $3x+1$$3x+1$3x+13 x+1$3x+1$ sequence ends this way?
53 Fourth Fermat prime
56 $\pi$$\pi$pi\pi$\pi$
60 The 24 th Mersenne prime has this many digits
62 10th Pell number
63 ${\pi }^e$${\pi }^e$pi^(e)\pi^{e}${\pi }^e$
64 $30°-$$30°-$30°-30°-$30°-$ ___$°-$$°-$°-°-$°-$ ___$°$$°$°°$°$ right triangle
65 Has digit sum 20 and digit product 336
66 $a,b,c$$a,b,c$a,b,ca, b, c$a,b,c$ where $\frac{1449}{50}=a+\frac{1}{b+\frac{1}{c}}$$\frac{1449}{50}=a+\frac{1}{b+\frac{1}{c}}$(1449)/(50)=a+(1)/(b+(1)/(c))\frac{1449}{50}=a+\frac{1}{b+\frac{1}{c}}$\frac{1449}{50}=a+\frac{1}{b+\frac{1}{c}}$
67 In Mayan numerals:
$\stackrel{⋮}{\equiv }$$\stackrel{⋮}{\equiv }$-=^(vdots)\stackrel{\vdots}{\equiv}$\stackrel{⋮}{\equiv }$

68 Fourth perfect number
69 Hypotenuse of a Pythagorean triple with sides 27,560 and 64,791

DOWN

2 A fixed point of $f(x)=2x^{10}-23x$$f(x)=2x^{10}-23x$f(x)=2x^(10)-23 xf(x)=2 x^{10}-23 x$f(x)=2x^{10}-23x$
3 $3825/99=$$3825/99=$3825//99=3825 / 99=$3825/99=$ ___ . ___
4 $\lceil \sinh (9)\rceil$$\lceil \sinh (9)\rceil$|~sinh(9)~|\lceil\sinh (9)\rceil$\lceil \sinh (9)\rceil$
5 $11\cdot {10}^3(600+\sqrt[3]{e})$$11\cdot {10}^3(600+\sqrt[3]{e})$11*10^(3)(600+root(3)(e))11 \cdot 10^{3}(600+\sqrt[3]{e})$11\cdot {10}^3(600+\sqrt[3]{e})$
6 The Sophie Germain prime that generates the safe prime 81,527
7 An eigenvalue for $\left(\begin{array}{cc}2& 1\\ 3& -2\end{array}\right)$$\left(\begin{array}{cc}2& 1\\ 3& -2\end{array}\right)$([2,1],[3,-2])\left(\begin{array}{cc}2 & 1 \\ 3 & -2\end{array}\right)$\left(\begin{array}{cc}2& 1\\ 3& -2\end{array}\right)$
8 It is $1/9$$1/9$1//91 / 9$1/9$th its reverse
9 $45$$45$4545$45$th term in Padovan sequence, which starts $1,1,1$$1,1,1$1,1,11,1,1$1,1,1$ and $p_n=p_{n-2}+p_{n-3}$$p_n=p_{n-2}+p_{n-3}$p_(n)=p_(n-2)+p_(n-3)p_{n}=p_{n-2}+p_{n-3}$p_n=p_{n-2}+p_{n-3}$
10 XMMCLXXXIX
11 $e$$e$ee$e$
12 Number of ways to make change for a dollar without the $\mathrm{\$}1$$\mathrm{\$}1$$1\$ 1$\mathrm{\$}1$ coin
13 Emergency number in the UK
21 In Morse code:

22 Circumference of a circle of radius $9/14$$9/14$9//149 / 14$9/14$
26 Gelfond-Schneider constant: $2^{\sqrt{2}}$$2^{\sqrt{2}}$2^(sqrt2)2^{\sqrt{2}}$2^{\sqrt{2}}$
27 Zip code for Elkton, Minnesota (population 141)
28 It is CAB in hexadecimal
29 Slope of the tangent line to $y=\frac{1}{10}{x}^{10}-\ln x$$y=\frac{1}{10}{x}^{10}-\ln x$y=(1)/(10)x^(10)-ln xy=\frac{1}{10} x^{10}-\ln x$y=\frac{1}{10}{x}^{10}-\ln x$ at $x=2$$x=2$x=2x=2$x=2$
30 Fibonacci sequence starting with no rabbits
32 $1366$$1366$13661366$1366$th prime number
33 Diagonal of a regular pentagon with side-length $10$$10$1010$10$
34 $1+1/\pi$$1+1/\pi$1+1//pi1+1 / \pi$1+1/\pi$
35 A prime factor of $\mathrm{111,111,111,111,111,111,111,111,111,111}$$\mathrm{111,111,111,111,111,111,111,111,111,111}$111,111,111,111,111,111,111,111,111,111111{,}111{,}111{,}111{,}111{,}111{,}111{,}111{,}111{,}111$\mathrm{111,111,111,111,111,111,111,111,111,111}$
37 Append any of its digits to the end and it is prime
40 In Chinese counting rods:

43 Fifth Mersenne prime
45 ${\int }_0^{10}\frac{1}{2\sqrt{x}}dx$${\int }_0^{10} \frac{1}{2\sqrt{x}}dx$int_(0)^(10)(1)/(2sqrtx)dx\int_{0}^{10} \frac{1}{2 \sqrt{x}} d x${\int }_0^{10}\frac{1}{2\sqrt{x}}dx$
48 Number of sequences of 20 coin tosses starting with heads
51 $i^i$$i^i$i^(i)i^{i}$i^i$
52 In Babylonian cuneiform:
53 $e^{\pi }$$e^{\pi }$e^(pi)e^{\pi}$e^{\pi }$
54 Number of 5-letter codes made from A through K with no repetition
55 It is $10011001100000111$$10011001100000111$1001100110000011110011001100000111$10011001100000111$ in binary
57 Fourth row of Pascal's triangle
58 Euler-Mascheroni constant: $\gamma =0$$\gamma =0$gamma=0\gamma=0$\gamma =0$. ___.
59 Feet in a mile
60 Devil's number
61 James Bond's number