{1  {:pegged true, :connections {6 3, 4 2}},
2  {:pegged true, :connections {9 5, 7 4}},
3  {:pegged true, :connections {10 6, 8 5}},
4  {:pegged true, :connections {13 8, 11 7, 6 5, 1 2}},
5  {:pegged true, :connections {14 9, 12 8}},
6  {:pegged true, :connections {15 10, 13 9, 4 5, 1 3}},
7  {:pegged true, :connections {9 8, 2 4}},
8  {:pegged true, :connections {10 9, 3 5}},
9  {:pegged true, :connections {7 8, 2 5}},
10 {:pegged true, :connections {8 9, 3 6}},
11 {:pegged true, :connections {13 12, 4 7}},
12 {:pegged true, :connections {14 13, 5 8}},
13 {:pegged true, :connections {15 14, 11 12, 6 9, 4 8}},
14 {:pegged true, :connections {12 13, 5 9}},
15 {:pegged true, :connections {13 14, 6 10}},
:rows 5}

      1
     2 3
    4 5 6
  7  8 9 10
11 12 13 14 15

(defn tri*  "Generates lazy sequence of triangular numbers"
([] (tri* 0 1))
([sum n]
(let [new-sum (+ sum n)]
(cons new-sum (lazy-seq (tri* new-sum (inc n)))))))

(def tri (tri*))
(take 5 tri)
; => (1 3 6 10 15)

(defn triangular?
"Is the number triangular? e.g. 1, 3, 6, 10, 15, etc"
[n]
(= n (last (take-while #(>= n %) tri))))

(triangular? 5)
; => false

(triangular? 6); => true

(defn row-tri
"The triangular number at the end of row n"
[n]
(last (take n tri)))

(row-tri 1); => 1
(row-tri 2); => 3
(row-tri 3); => 6

(defn row-num
"Returns row number the position belongs to: pos 1 in row 1,  positions 2 and 3 in row 2, etc"
[pos]
(inc (count (take-while #(> pos %) tri))))

(row-num 1)
; => 1
(row-num 5)
; => 3

(defn connect
"Form a mutual connection between two positions"
[board max-pos pos neighbor destination]
(if (<= destination max-pos)
(reduce (fn [new-board [p1 p2]]
(assoc-in new-board [p1 :connections p2] neighbor))
board   [[pos destination] [destination pos]])    board))

(connect {} 15 1 2 4)
; => {1 {:connections {4 2}}      4 {:connections {1 2}}}

(assoc-in {} [:cookie :monster :vocals] "Finntroll")
; => {:cookie {:monster {:vocals "Finntroll"}}}

(get-in {:cookie {:monster {:vocals "Finntroll"}}} [:cookie :monster])
; => {:vocals "Finntroll"}

(assoc-in {} [1 :connections 4] 2)
; => {1 {:connections {4 2}}}