Working in Pairs

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Getting everybody to work one-to-one with everyone else during a course is one of those tasks that you think should be easy to arrange, but when you try to work out the pairings, the combinations never quite seem to work.

One common attempt to deal with this problem in introductions is to divide the group in two and form two concentric circles with the same number of participants in each circle—the people in the inner circle facing outwards and the people in the outer circle facing inwards. The inner circle remains stationary, and the outer circle moves one person anticlockwise every 30 seconds.

Although everyone from one circle will have met everyone from the other circle, this exercise does not introduce everyone to everyone else. This can be done, but it is a bit tricky to work out. You'll be pleased to know that this resource gives all the combinations for 3-24 people.

The number of possible pairings in a group of n people is:

n(n-1)/2

Everyone will have met everyone else in n-1 rounds for an even number of people and n rounds for an odd number of people.

The table rows represent one round, with the letters representing individual people. There can only be "perfect" solutions for even numbers of people. If you have an odd number, either set a task for people who are not paired (*) or use a facilitator to make up the pairs.

3 People
1	AB	C*
2	AC	B*
3	A*	BC

4 People
1	AB	CD
2	AC	BD
3	AD	BC

5 People
1	AB	CD	E*
2	AC	BE	D*
3	AD	B*	CE
4	AE	BD	C*
5	A*	BC	DE

6 People
1	AB	CD	EF
2	AC	BE	DF
3	AD	BF	CE
4	AE	BD	CF
5	AF	BC	DE

7 People
1	AB	CD	EF	G*
2	AC	BD	EG	F*
3	AD	BC	E*	FG
4	AE	BF	CG	D*
5	AF	BE	C*	DG
6	AG	B*	CE	DF
7	A*	BG	CF	DE

8 People
1	AB	CD	EF	GH
2	AC	BD	EG	FH
3	AD	BC	EH	FG
4	AE	BF	CG	DH
5	AF	BE	CH	DG
6	AG	BH	CE	DF
7	AH	BG	CF	DE

9 People
1	AB	CD	EF	GH	I*
2	AC	BD	EG	FI	H*
3	AD	BC	EH	F*	GI
4	AE	BF	CG	D*	HI
5	AF	BE	CH	DI	G*
6	AG	BH	C*	DF	EI
7	AH	BI	CF	DG	E*
8	AI	B*	CE	DH	FG
9	A*	BG	CI	DE	FH

10 People
1	AB	CD	EF	GH	IJ
2	AC	BD	EG	FI	HJ
3	AD	BC	EH	FJ	GI
4	AE	BF	CG	DJ	HI
5	AF	BE	CH	DI	GJ
6	AG	BH	CJ	DF	EI
7	AH	BI	CF	DG	EJ
8	AI	BJ	CE	DH	FG
9	AJ	BG	CI	DE	FH

11 People
1	AB	CD	EF	GH	IJ	K*
2	AC	BE	DF	GI	HK	J*
3	AD	BF	CE	GJ	H*	IK
4	AE	BD	CF	GK	HJ	I*
5	AF	BC	DE	G*	HI	JK
6	AG	BH	CI	DJ	EK	F*
7	AH	BI	CJ	DK	E*	FG
8	AI	BJ	CK	D*	EG	FH
9	AJ	BK	C*	DG	EH	FI
10	AK	B*	CG	DH	EI	FJ
11	A*	BG	CH	DI	EJ	FK

12 People
1	AB	CD	EF	GH	IJ	KL
2	AC	BE	DF	GI	HK	JL
3	AD	BF	CE	GJ	HL	IK
4	AE	BD	CF	GK	HJ	IL
5	AF	BC	DE	GL	HI	JK
6	AG	BH	CI	DJ	EK	FL
7	AH	BI	CJ	DK	EL	FG
8	AI	BJ	CK	DL	EG	FH
9	AJ	BK	CL	DG	EH	FI
10	AK	BL	CG	DH	EI	FJ
11	AL	BG	CH	DI	EJ	FK

13 People
1	AB	CD	EF	GH	IJ	KL	M*
2	AC	BD	EG	FM	HJ	IK	L*
3	AD	BC	EL	FG	HK	IJ	M*
4	AE	BF	CG	DK	HL	IM	J*
5	AF	BE	CJ	DG	HM	IL	K*
6	AG	BI	CE	DF	H*	JL	KM
7	AH	BG	CF	DE	I*	JM	KL
8	AI	BJ	CK	DL	EM	F*	GH
9	AJ	BK	CL	DM	E*	FH	GI
10	AK	BL	CM	D*	EH	FI	GJ
11	AL	BM	C*	DH	EI	FJ	GK
12	AM	B*	CH	DI	EJ	FK	GL
13	A*	BH	CI	DJ	EK	FL	GM

14 People
1	AB	CD	EF	GH	IJ	KL	MN
2	AC	BD	EG	FM	HJ	IK	LN
3	AD	BC	EL	FG	HK	IJ	MN
4	AE	BF	CG	DK	HL	IM	JN
5	AF	BE	CJ	DG	HM	IL	KN
6	AG	BI	CE	DF	HN	JL	KM
7	AH	BG	CF	DE	IN	JM	KL
8	AI	BJ	CK	DL	EM	FN	GH
9	AJ	BK	CL	DM	EN	FH	GI
10	AK	BL	CM	DN	EH	FI	GJ
11	AL	BM	CN	DH	EI	FJ	GK
12	AM	BN	CH	DI	EJ	FK	GL
13	AN	BH	CI	DJ	EK	FL	GM

15 People
1	AB	CD	EF	GH	IJ	KL	MN	O*
2	AC	BD	EG	FH	IK	JL	MO	N*
3	AD	BC	EH	FG	IL	JK	M*	NO
4	AE	BF	CG	DH	IM	JN	KO	L*
5	AF	BE	CH	DG	IN	JM	K*	LO
6	AG	BH	CE	DF	IO	J*	KM	LN
7	AH	BG	CF	DE	I*	JO	KN	LM
8	AI	BJ	CK	DL	EM	FN	GO	H*
9	AJ	BK	CL	DM	EN	FO	G*	HI
10	AK	BL	CM	DN	EO	F*	GI	HJ
11	AL	BM	CN	DO	E*	FI	GJ	HK
12	AM	BN	CO	D*	EI	FJ	GK	HL
13	AN	BO	C*	DI	EJ	FK	GL	HM
14	AO	B*	CI	DJ	EK	FL	GM	HN
15	A*	BI	CJ	DK	EL	FM	GN	HO

16 People
1	AB	CD	EF	GH	IJ	KL	MN	OP
2	AC	BD	EG	FH	IK	JL	MO	NP
3	AD	BC	EH	FG	IL	JK	MP	NO
4	AE	BF	CG	DH	IM	JN	KO	LP
5	AF	BE	CH	DG	IN	JM	KP	LO
6	AG	BH	CE	DF	IO	JP	KM	LN
7	AH	BG	CF	DE	IP	JO	KN	LM
8	AI	BJ	CK	DL	EM	FN	GO	HP
9	AJ	BK	CL	DM	EN	FO	GP	HI
10	AK	BL	CM	DN	EO	FP	GI	HJ
11	AL	BM	CN	DO	EP	FI	GJ	HK
12	AM	BN	CO	DP	EI	FJ	GK	HL
13	AN	BO	CP	DI	EJ	FK	GL	HM
14	AO	BP	CI	DJ	EK	FL	GM	HN
15	AP	BI	CJ	DK	EL	FM	GN	HO

17 People
1	AB	CD	EF	GH	I*	JK	LM	NO	PQ
2	AC	BD	EG	FI	HQ	JL	KM	NP	O*
3	AD	BC	EH	FO	GI	JM	KL	NQ	P*
4	AE	BF	CG	DM	HI	JN	KO	LP	Q*
5	AF	BE	CH	DI	GP	JO	KN	LQ	M*
6	AG	BH	CL	DF	EI	JP	KQ	MO	N*
7	AH	BI	CF	DG	EN	JQ	K*	LO	MP
8	AI	BK	CE	DH	FG	J*	LN	MQ	OP
9	AJ	BG	CI	DE	FH	KP	L*	MN	OQ
10	AK	BL	CM	DN	EO	FP	GQ	H*	IJ
11	AL	BM	CN	DO	EP	FQ	G*	HJ	IK
12	AM	BN	CO	DP	EQ	F*	GJ	HK	IL
13	AN	BO	CP	DQ	E*	FJ	GK	HL	IM
14	AO	BP	CQ	D*	EJ	FK	GL	HM	IN
15	AP	BQ	C*	DJ	EK	FL	GM	HN	IO
16	AQ	B*	CJ	DK	EL	FM	GN	HO	IP
17	A*	BJ	CK	DL	EM	FN	GO	HP	IQ

18 People
1	AB	CD	EF	GH	IR	JK	LM	NO	PQ
2	AC	BD	EG	FI	HQ	JL	KM	NP	OR
3	AD	BC	EH	FO	GI	JM	KL	NQ	PR
4	AE	BF	CG	DM	HI	JN	KO	LP	QR
5	AF	BE	CH	DI	GP	JO	KN	LQ	MR
6	AG	BH	CL	DF	EI	JP	KQ	MO	NR
7	AH	BI	CF	DG	EN	JQ	KR	LO	MP
8	AI	BK	CE	DH	FG	JR	LN	MQ	OP
9	AJ	BG	CI	DE	FH	KP	LR	MN	OQ
10	AK	BL	CM	DN	EO	FP	GQ	HR	IJ
11	AL	BM	CN	DO	EP	FQ	GR	HJ	IK
12	AM	BN	CO	DP	EQ	FR	GJ	HK	IL
13	AN	BO	CP	DQ	ER	FJ	GK	HL	IM
14	AO	BP	CQ	DR	EJ	FK	GL	HM	IN
15	AP	BQ	CR	DJ	EK	FL	GM	HN	IO
16	AQ	BR	CJ	DK	EL	FM	GN	HO	IP
17	AR	BJ	CK	DL	EM	FN	GO	HP	IQ

19 People
1	AB	CD	EF	GH	IJ	KL	MN	OP	QR	S*
2	AC	BD	EG	FI	HJ	KM	LN	OQ	PS	R*
3	AD	BC	EH	FJ	GI	KN	LM	OR	P*	QS
4	AE	BF	CG	DJ	HI	KO	LP	MQ	N*	RS
5	AF	BE	CH	DI	GJ	KP	LO	MR	NS	Q*
6	AG	BH	CJ	DF	EI	KQ	LR	M*	NP	OS
7	AH	BI	CF	DG	EJ	KR	LS	MP	NQ	O*
8	AI	BJ	CE	DH	FG	KS	L*	MO	NR	PQ
9	AJ	BG	CI	DE	FH	K*	LQ	MS	NO	PR
10	AK	BL	CM	DN	EO	FP	GQ	HR	IS	J*
11	AL	BM	CN	DO	EP	FQ	GR	HS	I*	JK
12	AM	BN	CO	DP	EQ	FR	GS	H*	IK	JL
13	AN	BO	CP	DQ	ER	FS	G*	HK	IL	JM
14	AO	BP	CQ	DR	ES	F*	GK	HL	IM	JN
15	AP	BQ	CR	DS	E*	FK	GL	HM	IN	JO
16	AQ	BR	CS	D*	EK	FL	GM	HN	IO	JP
17	AR	BS	C*	DK	EL	FM	GN	HO	IP	JQ
18	AS	B*	CK	DL	EM	FN	GO	HP	IQ	JR
19	A*	BK	CL	DM	EN	FO	GP	HQ	IR	JS

20 People
1	AB	CD	EF	GH	IJ	KL	MN	OP	QR	ST
2	AC	BD	EG	FI	HJ	KM	LN	OQ	PS	RT
3	AD	BC	EH	FJ	GI	KN	LM	OR	PT	QS
4	AE	BF	CG	DJ	HI	KO	LP	MQ	NT	RS
5	AF	BE	CH	DI	GJ	KP	LO	MR	NS	QT
6	AG	BH	CJ	DF	EI	KQ	LR	MT	NP	OS
7	AH	BI	CF	DG	EJ	KR	LS	MP	NQ	OT
8	AI	BJ	CE	DH	FG	KS	LT	MO	NR	PQ
9	AJ	BG	CI	DE	FH	KT	LQ	MS	NO	PR
10	AK	BL	CM	DN	EO	FP	GQ	HR	IS	JT
11	AL	BM	CN	DO	EP	FQ	GR	HS	IT	JK
12	AM	BN	CO	DP	EQ	FR	GS	HT	IK	JL
13	AN	BO	CP	DQ	ER	FS	GT	HK	IL	JM
14	AO	BP	CQ	DR	ES	FT	GK	HL	IM	JN
15	AP	BQ	CR	DS	ET	FK	GL	HM	IN	JO
16	AQ	BR	CS	DT	EK	FL	GM	HN	IO	JP
17	AR	BS	CT	DK	EL	FM	GN	HO	IP	JQ
18	AS	BT	CK	DL	EM	FN	GO	HP	IQ	JR
19	AT	BK	CL	DM	EN	FO	GP	HQ	IR	JS

21 People
1	AB	CD	EF	GH	IJ	K*	LM	NO	PQ	RS	TU
2	AC	BE	DF	GI	HK	JU	LN	MP	OQ	RT	S*
3	AD	BF	CE	GJ	HS	IK	LO	MQ	NP	RU	T*
4	AE	BD	CF	GK	HJ	IT	LP	MO	NQ	R*	SU
5	AF	BC	DE	GR	HI	JK	LQ	MN	OP	ST	U*
6	AG	BH	CI	DJ	EK	FQ	LR	MS	NT	OU	P*
7	AH	BI	CJ	DK	EP	FG	LS	MT	NU	O*	QR
8	AI	BJ	CK	DO	EG	FH	LT	MU	N*	PR	QS
9	AJ	BK	CN	DG	EH	FI	LU	M*	OR	PS	QT
10	AK	BM	CG	DH	EI	FJ	L*	NR	OS	PT	QU
11	AL	BG	CH	DI	EJ	FK	MR	NS	OT	PU	Q*
12	AM	BN	CO	DP	EQ	FR	GS	HT	IU	J*	KL
13	AN	BO	CP	DQ	ER	FS	GT	HU	I*	JL	KM
14	AO	BP	CQ	DR	ES	FT	GU	H*	IL	JM	KN
15	AP	BQ	CR	DS	ET	FU	G*	HL	IM	JN	KO
16	AQ	BR	CS	DT	EU	F*	GL	HM	IN	JO	KP
17	AR	BS	CT	DU	E*	FL	GM	HN	IO	JP	KQ
18	AS	BT	CU	D*	EL	FM	GN	HO	IP	JQ	KR
19	AT	BU	C*	DL	EM	FN	GO	HP	IQ	JR	KS
20	AU	B*	CL	DM	EN	FO	GP	HQ	IR	JS	KT
21	A*	BL	CM	DN	EO	FP	GQ	HR	IS	JT	KU

22 People
1	AB	CD	EF	GH	IJ	KV	LM	NO	PQ	RS	TU
2	AC	BE	DF	GI	HK	JU	LN	MP	OQ	RT	SV
3	AD	BF	CE	GJ	HS	IK	LO	MQ	NP	RU	TV
4	AE	BD	CF	GK	HJ	IT	LP	MO	NQ	RV	SU
5	AF	BC	DE	GR	HI	JK	LQ	MN	OP	ST	UV
6	AG	BH	CI	DJ	EK	FQ	LR	MS	NT	OU	PV
7	AH	BI	CJ	DK	EP	FG	LS	MT	NU	OV	QR
8	AI	BJ	CK	DO	EG	FH	LT	MU	NV	PR	QS
9	AJ	BK	CN	DG	EH	FI	LU	MV	OR	PS	QT
10	AK	BM	CG	DH	EI	FJ	LV	NR	OS	PT	QU
11	AL	BG	CH	DI	EJ	FK	MR	NS	OT	PU	QV
12	AM	BN	CO	DP	EQ	FR	GS	HT	IU	JV	KL
13	AN	BO	CP	DQ	ER	FS	GT	HU	IV	JL	KM
14	AO	BP	CQ	DR	ES	FT	GU	HV	IL	JM	KN
15	AP	BQ	CR	DS	ET	FU	GV	HL	IM	JN	KO
16	AQ	BR	CS	DT	EU	FV	GL	HM	IN	JO	KP
17	AR	BS	CT	DU	EV	FL	GM	HN	IO	JP	KQ
18	AS	BT	CU	DV	EL	FM	GN	HO	IP	JQ	KR
19	AT	BU	CV	DL	EM	FN	GO	HP	IQ	JR	KS
20	AU	BV	CL	DM	EN	FO	GP	HQ	IR	JS	KT
21	AV	BL	CM	DN	EO	FP	GQ	HR	IS	JT	KU

23 People

24 People

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